#Read file
airbnb <- read.csv("https://raw.githubusercontent.com/athursland/STA-210/master/airbnb.csv?fbclid=IwAR0ffZSvoMPWxJjX-a4gWp2UlripEqAK0NJtu2ioHgmG0uWjCm20Hse8pNw")

Data Preparation

#Make new variable has_reviews
airbnb <- airbnb %>% 
  mutate(has_reviews = case_when( 
    number_of_reviews == 0 ~ 0, 
    number_of_reviews > 0 ~ 1)
  )

#Make NAs = 0 for security_deposit
airbnb <- airbnb %>% 
  mutate(security_deposit = if_else(is.na(security_deposit),0,security_deposit))

#Make NAs = 0 for cleaning_fee
airbnb <- airbnb %>% 
  mutate(cleaning_fee = if_else(is.na(cleaning_fee),0,cleaning_fee))

#Make NAs = 0 for review_scores_rating
airbnb <- airbnb %>% 
  mutate(review_scores_rating = case_when(
    is.na(review_scores_rating) ~ 0, 
    !is.na(review_scores_rating) ~ review_scores_rating)
    )

#Make NAs = 0 for review_scores_accuracy
airbnb <- airbnb %>% 
  mutate(review_scores_accuracy = case_when(
    is.na(review_scores_accuracy) ~ 0, 
    !is.na(review_scores_accuracy) ~ review_scores_accuracy)
    )

#Make NAs = 0 for review_scores_cleanliness
airbnb <- airbnb %>% 
  mutate(review_scores_cleanliness = case_when( 
    is.na(review_scores_cleanliness) ~ 0, 
    !is.na(review_scores_cleanliness) ~ review_scores_cleanliness)
    )

#Make NAs = 0 for review_scores_checkin
airbnb <- airbnb %>% 
  mutate(review_scores_checkin = case_when( 
    is.na(review_scores_checkin) ~ 0, 
    !is.na(review_scores_checkin) ~ review_scores_checkin)
    )

#Make NAs = 0 for review_scores_communcation
airbnb <- airbnb %>% 
  mutate(review_scores_communication = case_when( 
    is.na(review_scores_communication) ~ 0, 
    !is.na(review_scores_communication) ~ review_scores_communication)
    )

#Make NAs = 0 for review_sores_location 
airbnb <- airbnb %>% 
  mutate(review_scores_location = case_when( 
    is.na(review_scores_location) ~ 0, 
    !is.na(review_scores_location) ~ review_scores_location)
    )

#Make NAs = 0 for review_scores_value
airbnb <- airbnb %>% 
  mutate(review_scores_value = case_when( 
    is.na(review_scores_value) ~ 0, 
    !is.na(review_scores_value) ~ review_scores_value)
    )

#Make NAs = 0 for reviews_per_month
airbnb <- airbnb %>% 
  mutate(reviews_per_month = case_when( 
    is.na(reviews_per_month) ~ 0, 
    !is.na(reviews_per_month) ~ reviews_per_month)
    )
#Log transform reviews_per_month
airbnb <- airbnb %>% 
  mutate(reviews_per_month.1 = reviews_per_month + 1,
  log.reviews_per_month = log(reviews_per_month.1))

#Log transform review_scores_rating
airbnb <- airbnb %>% 
  mutate(review_scores_rating.1 = review_scores_rating + 1,
  log.review_scores_rating = log(review_scores_rating.1))

#Log transform reviews_scores_value
airbnb <- airbnb %>% 
  mutate(review_score_value.1 = review_scores_value + 1,
  log.review_scores_value = log(review_score_value.1))

#Log transform review_scores_location
airbnb <- airbnb %>% 
  mutate(review_scores_location.1 = review_scores_location + 1,
  log.review_scores_location = log(review_scores_location.1))

#Log transform review_scores_communication
airbnb <- airbnb %>% 
  mutate(review_scores_communication.1 = review_scores_communication + 1,
  log.review_scores_communication = log(review_scores_communication.1))

#Log transform review_scores_checkin
airbnb <- airbnb %>% 
  mutate(review_scores_checkin.1 = review_scores_checkin + 1,
  log.review_scores_checkin = log(review_scores_checkin.1))

#Log transform review_scores_accuracy
airbnb <- airbnb %>% 
  mutate(review_scores_accuracy.1 = review_scores_accuracy + 1,
  log.review_scores_accuracy = log(review_scores_accuracy.1))

#Log transform review_scores_cleanliness
airbnb <- airbnb %>% 
  mutate(review_scores_cleanliness.1 = review_scores_cleanliness + 1,
  log.review_scores_cleanliness = log(review_scores_cleanliness.1))

#Make NAs = 0 for host_response_rate
#airbnb <- airbnb %>% 
  #mutate(host_response_rate = case_when( 
    #is.na(host_response_rate) ~ 0.0, 
    #!is.na(host_response_rate) ~ host_response_rate)
    #)
#Make price as numeric
airbnb$price <- as.numeric(as.character(airbnb$price))
## Warning: NAs introduced by coercion
airbnb$price
##    [1]  55 765 225  77  75 220 107  71  26 125 134  58  65  60  68  60 100
##   [18] 250  50 279 100  76 125 115 119  95  95  47  50 130 135 155 119  30
##   [35]  75  49  45  49 250 309 175  99 224 137  65  95  62 200 115 145 130
##   [52] 442  95  90  55 135  68  60  72 115 250 110  85 765 331  95  NA  57
##   [69]  70  75  90  88  96  80 175 110 118 144  90 192  70  75 150  44  89
##   [86]  80 275  55  60  99  87  79  89 216  60  28 109 150  48  88  99  89
##  [103] 165  60 130 120  53 199  49  85  50  78  85 165  85  89 100 140 100
##  [120]  NA 375  79 195 205  65  79 668 190  77 135 100  97 160 105 110 135
##  [137] 160 176  48  29 199  68 140  99  39 136 140  75 279  75 120 245 100
##  [154]  59  65  70  97  51  96 119 110  90 125  75 135 275  37 125 245 120
##  [171]  79  59  90 195  77  89  88 325  75  40 145 280 197  99  99  68  69
##  [188] 240 199  70  65  65 125  99  60  70  75  88 129  59  80  52  86  75
##  [205]  49 150 200 195  50 175  65  90 125 134 220 125  95  84  80 250  80
##  [222] 101 127 275 130 180 115  65 250  49  89  70  95  98 155 700  75 310
##  [239]  49  60  42 129 115  98 175 485  75  83 199  50 160  60  65  55  74
##  [256]  90 150  86  49  50 125 219 110  40  80  66  75 100  99 105 250  65
##  [273]  52  89  95 125  79 115  89  92 110 120  95 145  52 150 130  85 140
##  [290]  53 115  27  72  47  89 115 350  78 107  55  89  79  99  56 125 115
##  [307]  95 111  75  75  99  75 117 195  99  88 115  83  55  95  90  85  95
##  [324]  50 149  59  39 240  85  95  80  60  90 125  52 105 250  85  50 220
##  [341] 214  60 200  70 300  47 266  99 195 111  95 169 200  49  60  70  99
##  [358]  85  70 130  57 149 100  65 200  89 190 145  39 250 110 120 195  87
##  [375] 100  90 120 175 129  95  98  80 119 285  88 100  75  35  75  55 200
##  [392]  75 110  70  84  89 240  28  70  39  80 115 140  40  85  75 100 290
##  [409]  80  49  65 199  95 125 199  73 275 180 195 109 127  62  55 125  90
##  [426] 125 219 135  90 230  99  60  69 195  75  89  65 119  79  95 175  90
##  [443] 175 110  70 150 139 109 130  75  76 630 113 149 125 158  50 149  86
##  [460]  92  99  40 170  95 100  64 249 125 109 150 105  80 125  99  44 124
##  [477]  69  95 125 125 290 205  61 235  46  27  75 110 325 199 425 100 375
##  [494]  85 125 147 175  80  49  89  49  67 225 125  40 110 100  60  66 148
##  [511] 142 130  89  90 125  88 135  69 115  82 450  27 775 175 119 129  NA
##  [528] 240 129 109  92 145 199 112  81  95 110 190 170 135 172  60  55  52
##  [545]  80 125 300 150  55  55  59  75 145  80 150 155  69  91  85  60 130
##  [562] 120  60  75  98  70 219 125 160  95 225 119 115  70 219 219 170 125
##  [579]  59  75 144  61  55  59  51 350 150  30 165 150  80  55 127  85  40
##  [596] 250  80 145 120 145 250 125  50 124  51 165  95  70 139 250  79  95
##  [613]  50  85 121 110  40 100  75  79 165  70  95 199  63  67 129  90  40
##  [630]  50 125 150  82 120  80  45 100 266  59  97  47 140 124  80  99 150
##  [647] 150 100  48 125  80 150  56  80  49 249  48 160 130  99  56 450 141
##  [664]  95  48 150 240 110 150 106 500  90 220 130  95  89  85 110  99 149
##  [681]  90 150 125 105 120  90  77 131  70 185  60 125  62  89  85  67  74
##  [698]  40  75  84  85 167  85 149  89 125  80 495 150 100  90  33  59  88
##  [715] 110  50 120 243  89  90 145 295  90  50 250 115  45  95  54  75 160
##  [732]  95 130  55 165 125  36  57  99  95  79 145  51  45  30 112  80 200
##  [749]  40  79  65 275  80 225 135  60 230 149  45  71 285 500  76 125  60
##  [766] 140  90 120 165 135  79 125 100 135  22  40 109 162  62 105  66  37
##  [783] 172  99 100  88 195  50 128 220 210  98 149 445  90  99 100 100 129
##  [800]  80 124 137 119 310 109 159 169 350  85  60 330 150 120 359  92  34
##  [817] 175  50  69 250 200 150 275 225  46 900 450 450 450 335 335 275 775
##  [834] 500 450  NA 149  35  89  55 125  78  40  70  99 129  75 115  62 375
##  [851] 185 175 199  85  75  92 250 225 250  54  58  38  65  95  52  92 600
##  [868] 350 225  99 200 120  74  80  87 110 124  99  85  55 120 119  62  60
##  [885] 100  90  85  95 176 135 465  58 465 930 180 130 125  80 150 145 100
##  [902] 225  45 111 249  60  90  90 125  90  80  75 100  86 105 199  89  79
##  [919]  60 120 125 129 115  60 700  38  82 175  75  70  70  70  70  70 198
##  [936]  80  90  45  90  72 128  92  70  65  85  70  70  70  90 145  95  62
##  [953]  85  76  90  74 250  69  NA  65  95  80  90  69 119  75  79  73  60
##  [970]  35 249 270  62 600 289  55  55  48  99 105 149 125 200 125  45 109
##  [987]  84  79  60  79  79 250 110 105 525  78 125  85  91  65 167  80 150
## [1004] 175  82 300 150 375  70  42  69  65  70 330 110  95 125 160 200 110
## [1021] 285 188 175  90 285  59  65  95 195 170  89  38 120  99 184 225 125
## [1038] 100  84  75 125 179  80 165 259  75  75 115  64  95 135  99  70  65
## [1055]  52  65  47 120  62 120  49 355  50  51  58 185 125 150  72  55  89
## [1072]  93  65 149  59  70 200  65 165 375  75  60  75 285 125  95 225  85
## [1089]  80  85  95 200  40  45 125 119 149  61  70 110  85 150 110  85  81
## [1106] 160  99  50 250  65 245 125  95 289  68 105 135  30 330 102  70  96
## [1123]  70  90  75 144  63 195 135  98  42 150 200  85 250 310  60 159  49
## [1140]  68  50 125  89 925 129 115 138  93 175 105 195 100  39 320  70  40
## [1157] 325 335  85 185  69  90  10  95 169 199  99  60  99  75 295  75 125
## [1174] 325 107  62 250  70  45  78 125  68  57 145  99 130  39 109  80 115
## [1191]  20 135  80 125 250 100 150 120  99  85 145 135  65  50  77  57 155
## [1208]  70  85 140 110  79  70  85  49 300 150  87 130 100  75 700  88  97
## [1225]  87 175 100 150 115 120  80 150  51  51  80  60 375  49 125 125  80
## [1242] 125  60 140  99  49  25 165  89 305  89  63  39  69 100  69  60 149
## [1259] 265 350  43 305  75  65 100  95  80 185  33  98 125 119 135 135  79
## [1276]  90 100  43 115 100  96 225 115  75  50 375 125 500 195  90 140 100
## [1293] 100 110  75 225  50 125  75 150  99 125 225 150  55  99 105  79 195
## [1310]  57 225  95  40  40 180  63 110  65 199  50 195 200  99  63 185 211
## [1327] 110  55 150  50 119  99 125 175 210  39 150  65  90  61 100 111 100
## [1344] 150 190  72  68  70 140 120 250 179 127  95  32  30 199  69  90  97
## [1361]  90  45  45 130  69 100  60 120 120 100 125 120  40 160 175  95  65
## [1378] 129  80 544 375 190 175 165  35 320  35 295 135  77  71  55  75 114
## [1395] 119  60 180  50  40 101  91  80 134  68  90 125  40  75  38 125 395
## [1412] 150  60  60 105  75 110 400  63  70 106 250 115  60 229 120  65 100
## [1429] 195 127 150  55  80 175  90  90  50  80 120 500  43  70  85  62  85
## [1446]  52  24 299  80  68 120  37 115 139  84 157  89 225 125  73  99 266
## [1463]  90  99 385  75  59  68  80  60 150 195 199 135  55 275 150 200 125
## [1480] 145 210  85 225  NA  55 768  40  56 200  80  70 179  89  89  86 238
## [1497] 130 238 238 266 268 975 750  NA 155  40  75  65  90 195 165  74 223
## [1514] 101  46  79  75  11 106  95 125 115 168 199  95 275  92 175  75 250
## [1531]  95  99  65 100 105  82  58 110  75 240 109  50  75 150  69  80 120
## [1548] 119 250  99 250 100  99  85  99 100  62 480  75  69  75 106  49 129
## [1565] 215 100  75  85  70 145 110  40  17  68 100 195  50 100 120 275  80
## [1582] 100  89  99  90  65  62  89 185 150  95 100 155 285 100  40  65  71
## [1599] 105 585 119 225  41  70  24  50 399 125 250  17  75 200 129 180 115
## [1616] 240  60 250 425  85  50 177 200  19 150 110  99 149  65 178  80  88
## [1633]  60  79  99  75  85 144  60 250 250  75 225  55  35  99  NA 200 350
## [1650]  79 100 100  75 108  90  80  50 279 110 185  58  80  75 350  50 199
## [1667]  75 248  64 100  50  44  92  45  65 162  79 186  75  40  95  50 150
## [1684] 180 225  69  19  65  73 200 250  45 275  25 165  56 125  92  75 115
## [1701] 125  90  95  85  49  55  90 300  19 118 104 190  85  85 495 300  68
## [1718]  60  64  65  79 140 249 100  89  55 175 250  95  57  95  69 325  76
## [1735] 375 375 175  71 595  90 155 165  74  58  49 155  35  90 675  92 100
## [1752]  80 195 145  77 100  58 198 115  75 124 225  65 250 200 145 275  42
## [1769] 450  44  88 175 115  53 206  57  65 300  88  75  93 130  95 265  49
## [1786]  90 198  67 130  96 500  85  80  80  74 119 228  96 530 426  88 147
## [1803]  61 150 125 250 222  60  79 800 150 205  63  50 195 414 120  NA 377
## [1820] 509 175  85 150  59  50  75 469 399  89  80 205 375 611 255 255 100
## [1837] 425  NA 150  84  58  77 150  75 219  65  75  40 228  79 117 195 115
## [1854]  65 150  45  94 139  93 120 225  91 145  73  75  60 168 101  55 150
## [1871]  56  65  50 225  88  47 125  69  59  99 225 180 135  49  85  70 129
## [1888] 199  25 159 199  75  59 110  75 250 130 450 175  78  89 260 239  25
## [1905]  98  80 109  95 145  60  88  96  99  50  44  90 120  22 412 820 482
## [1922]  50 401 413  42 391 253 224 239 239 199  90  NA  60 110
#Make host_response_rate as numeric
#airbnb$host_response_rate <- as.character(sub("%", "", airbnb$host_response_rate))
#airbnb$host_response_rate <- as.numeric(airbnb$host_response_rate)
#airbnb$host_response_rate
#Make zipcode a factor
airbnb$zipcode <- as.factor(airbnb$zipcode)
#Omit all observations with NAs 
airbnb <- airbnb[complete.cases(airbnb),]

Separate training and testing

#80% of the sample size
smp_size <- floor(0.80 * nrow(airbnb))

#set the seed to make your partition reproducible
set.seed(123456)
train_ind <- sample(seq_len(nrow(airbnb)), size = smp_size)

train.airbnb <- airbnb[train_ind, ]
test.airbnb <- airbnb[-train_ind, ]
train.airbnb <- train.airbnb %>% mutate(log.bathrooms = log(bathrooms),
                            log.securitydeposit = log(security_deposit),
                            log.guestsincluded = log(guests_included),
                            log.nreviews = log(number_of_reviews))

Description of data

Question of interest: How can we produce a model that accurately predicts the listed nightly price for an Airbnb in Asheville, NC?

The data set we are using is a .csv file of every AirBnB listing in the city of Asheville, North Carolina as of October 17, 2018 . Each observation is an individual listing. We sourced this data from Inside AirBnB, a website that regularly scrapes data from AirBnB’s listings and provides them as public data sets separated by city.

The original data set was very large (96 columns and 1,936 observations), so we reduced it for simplicity’s sake. We chose 26 columns that could potentially be of interest for a regression analysis, and we created one more column called has_reviews, which is an indicator variable. We noticed that some columns, like cleaning_fee and security_deposit, had a lot of NAs, so instead of omitting all of these observations we mutated NAs from these columns to be 0s. We were left with 24 incomplete cases, likely the result of web scraping errors, and so we chose to omit them. Our final number of columns was 27 and our final number of rows was 1,911.

Variables: * host_response_rate * host_is_superhost * host_listings_count * zipcode * property_type * room_type * accomodates * bathrooms * beds * bed_type * price * security_deposit * cleaning_fee * guests_included * extra_people_cost * minimum_nights * maximum_nights * availability_30 * number_of_reviews * review_scores_rating * review_scores_accuracy * review_scores_cleanliness * review_scores_checkin * review_scores_communication * review_scores_location * review_scores_value * reviews_per_month * cancellation_policy

Background

Airbnb, inc. is a privately held global company headquartered in San Francisco that operates as a broker for lodging arrangements. Made famous by celebrities like Kim Kardashian, the company is revolutionizing the way people vacation. Rather than booking a hotel, users can go on the AirBnB website or mobile app and quickly rent private rooms, guest suites or even entire homes to themselves. The company has often faced controversy surrounding housing affordability, pricing transparency, privacy and hotel industry competition. Despite these concerns, it blew by its own internal forecasts and brought in 2.6 billion dollars in revenue and 93 million in profit by the end of 2017. For a company that exclusively makes money by taking a small commission (3%) of the price of every listing, that’s pretty impressive.

We were interested in this data because it’s something that so many people, especially our peers here at Duke, would find relevant. There are over 4 million AirBnB listings worldwide and 150 million global users. Both Mary Helen and I have stayed in an AirBnB in the last month. With the option to rent entire homes, AirBnBs offer more luxury, space and solitude than other lodging options. Hosts set prices for listings at their own discretion, and so there isn’t any specific algorithm or model by which it’s calculated. By using this data to create a model that can accurately predict prices for listings, we might be able to help people figure out what the typical price range is for the type of listing they want – and therefore, whether or not a specific listing is a good deal. Specifically, we’ll be looking at AirBnB listings in the Asheville Metro Area, North Carolina. Asheville is a popular weekend getaway in North Carolina. Given its relative proximity to Duke, many students visit at least once during their time here – often staying in AirBnBs when they do. This makes our data more relevant to our peers, and also helps us by narrowing down the total number of observations into a size that’s more manageable.

Exploratory Data Analysis

#Pairs plots for all of the explanatory variables
pairs(price ~ host_response_rate + host_is_superhost + host_listings_count, data=train.airbnb)
<<<<<<< HEAD

pairs(price ~ zipcode + room_type + bathrooms, data=train.airbnb)

pairs(price ~ accommodates + beds + bed_type, data=train.airbnb)

pairs(price ~ security_deposit + cleaning_fee + guests_included, data = train.airbnb)

pairs(price ~ extra_people + minimum_nights + availability_30, data = train.airbnb)

pairs(price ~ number_of_reviews + review_scores_rating + review_scores_accuracy, data = train.airbnb)

pairs(price ~ review_scores_cleanliness + review_scores_checkin + review_scores_communication, data = train.airbnb)

pairs(price ~ review_scores_location + review_scores_value + reviews_per_month, data = train.airbnb)

pairs(price ~ cancellation_policy, data = train.airbnb)

#Pairs with log.bathrooms, log.cleaningfee, log.securitydeposit, log.guestsincluded, log.nreviews
pairs(price ~ log.securitydeposit + log.guestsincluded + log.nreviews, data = train.airbnb)

#Distribution of nightly price
ggplot(train.airbnb, aes(x=price)) + geom_histogram(stat="count")

#Boxplot of price by bed type
ggplot(train.airbnb, aes(x=bed_type, y=price)) + geom_boxplot()

=======

pairs(price ~ zipcode + room_type + bathrooms, data=train.airbnb)

pairs(price ~ accommodates + beds + bed_type, data=train.airbnb)

pairs(price ~ security_deposit + cleaning_fee + guests_included, data = train.airbnb)

pairs(price ~ extra_people + minimum_nights + availability_30, data = train.airbnb)

pairs(price ~ number_of_reviews + review_scores_rating + review_scores_accuracy, data = train.airbnb)

pairs(price ~ review_scores_cleanliness + review_scores_checkin + review_scores_communication, data = train.airbnb)

pairs(price ~ review_scores_location + review_scores_value + reviews_per_month, data = train.airbnb)

pairs(price ~ cancellation_policy, data = train.airbnb)

#Pairs with log.bathrooms, log.cleaningfee, log.securitydeposit, log.guestsincluded, log.nreviews
pairs(price ~ log.bathrooms + log.cleaningfee, data = train.airbnb)

pairs(price ~ log.securitydeposit + log.guestsincluded + log.nreviews, data = train.airbnb)

#Distribution of nightly price
ggplot(train.airbnb, aes(x=price)) + geom_histogram(stat="count")

#Boxplot of price by bed type
ggplot(train.airbnb, aes(x=bed_type, y=price)) + geom_boxplot()

>>>>>>> 7908b9b1aeedc695e3fe7a5189806fcc47b5a031

Model building

NOTE -> we are omitting host_response_rate from our model because we were having trouble converting the variable to a numeric without losing a lot of the information. Will address before final due date.

full.model <- lm(price ~ host_is_superhost
+ host_listings_count
+ zipcode
+ room_type
+ accommodates
+ bathrooms
+ beds
+ bed_type
+ cleaning_fee
+ extra_people
+ minimum_nights
+ availability_30
+ number_of_reviews
+ log.review_scores_rating
+ log.review_scores_accuracy
+ log.review_scores_cleanliness
+ log.review_scores_checkin
+ log.review_scores_communication
+ log.review_scores_location
+ log.review_scores_value
+ log.reviews_per_month
+ cancellation_policy, data=train.airbnb)

kable(tidy(full.model), digits=3)
term estimate std.error statistic p.value
(Intercept) -6.939 36.364 -0.191 0.849
host_is_superhostt 6.008 3.731 1.610 0.108
host_listings_count 0.013 0.084 0.150 0.881
zipcode28715 -17.992 13.749 -1.309 0.191
zipcode28732 4.433 14.591 0.304 0.761
zipcode28748 -22.233 61.031 -0.364 0.716
zipcode28787 39.474 61.165 0.645 0.519
zipcode28801 42.285 8.269 5.114 0.000
zipcode28803 22.266 8.419 2.645 0.008
zipcode28804 29.145 8.632 3.377 0.001
zipcode28805 16.540 8.657 1.911 0.056
zipcode28806 4.091 7.865 0.520 0.603
zipcode28815 23.355 61.197 0.382 0.703
zipcode29710 -8.802 61.156 -0.144 0.886
room_typePrivate room -20.297 4.010 -5.062 0.000
room_typeShared room -79.926 23.747 -3.366 0.001
accommodates 13.099 1.622 8.076 0.000
bathrooms 43.293 3.816 11.347 0.000
beds -0.624 2.453 -0.254 0.799
bed_typeCouch 13.174 69.925 0.188 0.851
bed_typeFuton 31.961 41.827 0.764 0.445
bed_typePull-out Sofa 42.474 49.705 0.855 0.393
bed_typeReal Bed 32.667 35.033 0.932 0.351
cleaning_fee 0.308 0.048 6.420 0.000
extra_people 0.009 0.076 0.118 0.906
minimum_nights -2.077 0.212 -9.792 0.000
availability_30 0.560 0.202 2.773 0.006
number_of_reviews 0.014 0.026 0.544 0.586
log.review_scores_rating -24.040 12.841 -1.872 0.061
log.review_scores_accuracy -52.903 57.657 -0.918 0.359
log.review_scores_cleanliness 135.420 35.304 3.836 0.000
log.review_scores_checkin -62.905 60.622 -1.038 0.300
log.review_scores_communication -11.178 46.949 -0.238 0.812
log.review_scores_location 77.630 42.880 1.810 0.070
log.review_scores_value -43.160 39.570 -1.091 0.276
log.reviews_per_month -26.636 3.650 -7.297 0.000
cancellation_policymoderate 2.856 4.329 0.660 0.510
cancellation_policystrict_14_with_grace_period 11.439 4.766 2.400 0.017
cancellation_policysuper_strict_30 6.954 15.502 0.449 0.654
cancellation_policysuper_strict_60 206.731 14.862 13.910 0.000
backward.model <- ols_step_backward_aic(full.model, details=TRUE)
## Backward Elimination Method 
## ---------------------------
## 
## Candidate Terms: 
## 
## 1 . host_is_superhost 
## 2 . host_listings_count 
## 3 . zipcode 
## 4 . room_type 
## 5 . accommodates 
## 6 . bathrooms 
## 7 . beds 
## 8 . bed_type 
## 9 . cleaning_fee 
## 10 . extra_people 
## 11 . minimum_nights 
## 12 . availability_30 
## 13 . number_of_reviews 
## 14 . log.review_scores_rating 
## 15 . log.review_scores_accuracy 
## 16 . log.review_scores_cleanliness 
## 17 . log.review_scores_checkin 
## 18 . log.review_scores_communication 
## 19 . log.review_scores_location 
## 20 . log.review_scores_value 
## 21 . log.reviews_per_month 
## 22 . cancellation_policy 
## 
##  Step 0: AIC = 16814.84 
##  price ~ host_is_superhost + host_listings_count + zipcode + room_type + accommodates + bathrooms + beds + bed_type + cleaning_fee + extra_people + minimum_nights + availability_30 + number_of_reviews + log.review_scores_rating + log.review_scores_accuracy + log.review_scores_cleanliness + log.review_scores_checkin + log.review_scores_communication + log.review_scores_location + log.review_scores_value + log.reviews_per_month + cancellation_policy 
## 
## -----------------------------------------------------------------------------------------------------
## Variable                           DF       AIC         Sum Sq          RSS        R-Sq     Adj. R-Sq 
## -----------------------------------------------------------------------------------------------------
## extra_people                       1     16812.857        50.894    5373806.868    0.688        0.680 
## host_listings_count                1     16812.866        81.238    5373837.212    0.688        0.680 
## log.review_scores_communication    1     16812.901       205.832    5373961.807    0.688        0.680 
## beds                               1     16812.909       235.055    5373991.029    0.688        0.680 
## number_of_reviews                  1     16813.147      1075.499    5374831.473    0.688        0.680 
## log.review_scores_accuracy         1     16813.707      3056.829    5376812.803    0.688        0.680 
## bed_type                           1     16807.920      3809.540    5377565.514    0.688        0.680 
## log.review_scores_checkin          1     16813.948      3909.543    5377665.518    0.688        0.680 
## log.review_scores_value            1     16814.064      4319.592    5378075.566    0.688        0.680 
## host_is_superhost                  1     16815.504      9415.425    5383171.399    0.687        0.679 
## log.review_scores_location         1     16816.205     11900.343    5385656.317    0.687        0.679 
## log.review_scores_rating           1     16816.438     12726.193    5386482.167    0.687        0.679 
## availability_30                    1     16820.718     27914.132    5401670.107    0.686        0.678 
## log.review_scores_cleanliness      1     16827.879     53423.437    5427179.411    0.685        0.677 
## room_type                          1     16844.527    120414.474    5494170.448    0.681        0.673 
## cleaning_fee                       1     16854.595    149655.892    5523411.866    0.679        0.671 
## log.reviews_per_month              1     16866.566    193329.879    5567085.853    0.677        0.668 
## accommodates                       1     16878.389    236800.138    5610556.112    0.674        0.666 
## zipcode                            1     16887.019    343479.206    5717235.180    0.668        0.662 
## minimum_nights                     1     16908.260    348148.667    5721904.641    0.668        0.659 
## bathrooms                          1     16939.630    467464.381    5841220.355    0.661        0.652 
## cancellation_policy                1     17003.873    743737.822    6117493.796    0.645        0.636 
## -----------------------------------------------------------------------------------------------------
## 
## 
## - bed_type 
## 
## 
##   Step 1 : AIC = 16807.92 
##  price ~ host_is_superhost + host_listings_count + zipcode + room_type + accommodates + bathrooms + beds + cleaning_fee + extra_people + minimum_nights + availability_30 + number_of_reviews + log.review_scores_rating + log.review_scores_accuracy + log.review_scores_cleanliness + log.review_scores_checkin + log.review_scores_communication + log.review_scores_location + log.review_scores_value + log.reviews_per_month + cancellation_policy 
## 
## -----------------------------------------------------------------------------------------------------
## Variable                           DF       AIC         Sum Sq          RSS        R-Sq     Adj. R-Sq 
## -----------------------------------------------------------------------------------------------------
## extra_people                       1     16805.935        54.003    5377619.517    0.688        0.681 
## host_listings_count                1     16805.944        84.086    5377649.600    0.688        0.681 
## log.review_scores_communication    1     16805.975       195.597    5377761.111    0.688        0.681 
## beds                               1     16805.991       251.115    5377816.629    0.688        0.681 
## number_of_reviews                  1     16806.218      1054.437    5378619.951    0.688        0.681 
## log.review_scores_accuracy         1     16806.815      3169.473    5380734.987    0.688        0.680 
## log.review_scores_checkin          1     16807.017      3882.429    5381447.943    0.688        0.680 
## log.review_scores_value            1     16807.115      4231.616    5381797.131    0.688        0.680 
## host_is_superhost                  1     16808.586      9442.094    5387007.608    0.687        0.680 
## log.review_scores_location         1     16809.288     11928.347    5389493.861    0.687        0.680 
## log.review_scores_rating           1     16809.487     12635.290    5390200.804    0.687        0.680 
## availability_30                    1     16813.992     28635.427    5406200.941    0.686        0.679 
## log.review_scores_cleanliness      1     16820.928     53358.800    5430924.314    0.685        0.677 
## room_type                          1     16838.107    122318.895    5499884.409    0.681        0.674 
## cleaning_fee                       1     16847.667    149741.472    5527306.986    0.679        0.672 
## log.reviews_per_month              1     16860.009    194806.406    5572371.920    0.676        0.669 
## accommodates                       1     16871.855    238403.004    5615968.518    0.674        0.666 
## zipcode                            1     16879.536    341612.375    5719177.889    0.668        0.663 
## minimum_nights                     1     16900.908    346778.760    5724344.274    0.668        0.660 
## bathrooms                          1     16932.517    467064.989    5844630.503    0.661        0.653 
## cancellation_policy                1     16996.975    744365.082    6121930.596    0.645        0.637 
## -----------------------------------------------------------------------------------------------------
## 
## - extra_people 
## 
## 
##   Step 2 : AIC = 16805.94 
##  price ~ host_is_superhost + host_listings_count + zipcode + room_type + accommodates + bathrooms + beds + cleaning_fee + minimum_nights + availability_30 + number_of_reviews + log.review_scores_rating + log.review_scores_accuracy + log.review_scores_cleanliness + log.review_scores_checkin + log.review_scores_communication + log.review_scores_location + log.review_scores_value + log.reviews_per_month + cancellation_policy 
## 
## -----------------------------------------------------------------------------------------------------
## Variable                           DF       AIC         Sum Sq          RSS        R-Sq     Adj. R-Sq 
## -----------------------------------------------------------------------------------------------------
## host_listings_count                1     16803.956        74.697    5377694.214    0.688        0.681 
## log.review_scores_communication    1     16803.990       194.984    5377814.502    0.688        0.681 
## beds                               1     16804.008       259.217    5377878.734    0.688        0.681 
## number_of_reviews                  1     16804.237      1066.749    5378686.266    0.688        0.681 
## log.review_scores_accuracy         1     16804.823      3143.560    5380763.078    0.688        0.681 
## log.review_scores_checkin          1     16805.037      3900.723    5381520.240    0.688        0.681 
## log.review_scores_value            1     16805.142      4271.024    5381890.541    0.688        0.681 
## host_is_superhost                  1     16806.631      9547.447    5387166.965    0.687        0.680 
## log.review_scores_location         1     16807.313     11962.843    5389582.360    0.687        0.680 
## log.review_scores_rating           1     16807.504     12642.745    5390262.262    0.687        0.680 
## availability_30                    1     16812.071     28859.823    5406479.341    0.686        0.679 
## log.review_scores_cleanliness      1     16818.936     53335.780    5430955.297    0.685        0.678 
## room_type                          1     16836.142    122392.325    5500011.842    0.681        0.674 
## cleaning_fee                       1     16846.048    151074.151    5528693.668    0.679        0.672 
## log.reviews_per_month              1     16858.177    195368.303    5572987.820    0.676        0.669 
## accommodates                       1     16870.376    240275.271    5617894.789    0.674        0.667 
## zipcode                            1     16877.638    341943.525    5719563.043    0.668        0.663 
## minimum_nights                     1     16899.040    347220.366    5724839.883    0.668        0.660 
## bathrooms                          1     16930.946    468659.215    5846278.732    0.661        0.653 
## cancellation_policy                1     16995.055    744632.148    6122251.665    0.645        0.637 
## -----------------------------------------------------------------------------------------------------
## 
## - host_listings_count 
## 
## 
##   Step 3 : AIC = 16803.96 
##  price ~ host_is_superhost + zipcode + room_type + accommodates + bathrooms + beds + cleaning_fee + minimum_nights + availability_30 + number_of_reviews + log.review_scores_rating + log.review_scores_accuracy + log.review_scores_cleanliness + log.review_scores_checkin + log.review_scores_communication + log.review_scores_location + log.review_scores_value + log.reviews_per_month + cancellation_policy 
## 
## -----------------------------------------------------------------------------------------------------
## Variable                           DF       AIC         Sum Sq          RSS        R-Sq     Adj. R-Sq 
## -----------------------------------------------------------------------------------------------------
## log.review_scores_communication    1     16802.019       222.956    5377917.170    0.688        0.681 
## beds                               1     16802.045       313.723    5378007.938    0.688        0.681 
## number_of_reviews                  1     16802.259      1071.375    5378765.590    0.688        0.681 
## log.review_scores_accuracy         1     16802.848      3156.239    5380850.454    0.688        0.681 
## log.review_scores_checkin          1     16803.047      3861.586    5381555.801    0.688        0.681 
## log.review_scores_value            1     16803.152      4230.816    5381925.030    0.688        0.681 
## host_is_superhost                  1     16804.633      9478.394    5387172.608    0.687        0.681 
## log.review_scores_location         1     16805.357     12044.103    5389738.318    0.687        0.680 
## log.review_scores_rating           1     16805.544     12708.748    5390402.963    0.687        0.680 
## availability_30                    1     16810.100     28888.894    5406583.108    0.686        0.679 
## log.review_scores_cleanliness      1     16816.952     53316.651    5431010.865    0.685        0.678 
## room_type                          1     16834.153    122356.977    5500051.191    0.681        0.674 
## cleaning_fee                       1     16848.722    168026.607    5545720.822    0.678        0.671 
## log.reviews_per_month              1     16856.177    195294.148    5572988.363    0.676        0.669 
## accommodates                       1     16868.854    241968.759    5619662.973    0.674        0.667 
## zipcode                            1     16875.739    342248.019    5719942.234    0.668        0.663 
## minimum_nights                     1     16897.548    349061.030    5726755.245    0.668        0.660 
## bathrooms                          1     16929.023    468884.147    5846578.362    0.661        0.653 
## cancellation_policy                1     17045.324    958746.108    6336440.323    0.632        0.625 
## -----------------------------------------------------------------------------------------------------
## 
## - log.review_scores_communication 
## 
## 
##   Step 4 : AIC = 16802.02 
##  price ~ host_is_superhost + zipcode + room_type + accommodates + bathrooms + beds + cleaning_fee + minimum_nights + availability_30 + number_of_reviews + log.review_scores_rating + log.review_scores_accuracy + log.review_scores_cleanliness + log.review_scores_checkin + log.review_scores_location + log.review_scores_value + log.reviews_per_month + cancellation_policy 
## 
## ---------------------------------------------------------------------------------------------------
## Variable                         DF       AIC         Sum Sq          RSS        R-Sq     Adj. R-Sq 
## ---------------------------------------------------------------------------------------------------
## beds                             1     16800.107       311.007    5378228.177    0.688        0.681 
## number_of_reviews                1     16800.321      1067.909    5378985.080    0.688        0.681 
## log.review_scores_accuracy       1     16801.048      3640.160    5381557.330    0.688        0.681 
## log.review_scores_value          1     16801.345      4693.817    5382610.988    0.687        0.681 
## log.review_scores_checkin        1     16801.864      6530.653    5384447.824    0.687        0.681 
## host_is_superhost                1     16802.682      9427.801    5387344.971    0.687        0.681 
## log.review_scores_location       1     16803.486     12280.357    5390197.527    0.687        0.681 
## log.review_scores_rating         1     16803.687     12991.612    5390908.783    0.687        0.680 
## availability_30                  1     16808.166     28901.526    5406818.696    0.686        0.680 
## log.review_scores_cleanliness    1     16815.086     53573.323    5431490.493    0.685        0.678 
## room_type                        1     16832.175    122212.902    5500130.072    0.681        0.674 
## cleaning_fee                     1     16846.821    168164.249    5546081.419    0.678        0.671 
## log.reviews_per_month            1     16854.257    195365.070    5573282.241    0.676        0.670 
## accommodates                     1     16866.985    242229.405    5620146.576    0.674        0.667 
## zipcode                          1     16873.791    342222.421    5720139.591    0.668        0.663 
## minimum_nights                   1     16895.701    349412.837    5727330.008    0.667        0.661 
## bathrooms                        1     16927.028    468679.816    5846596.986    0.661        0.653 
## cancellation_policy              1     17043.331    958552.392    6336469.563    0.632        0.625 
## ---------------------------------------------------------------------------------------------------
## 
## - beds 
## 
## 
##   Step 5 : AIC = 16800.11 
##  price ~ host_is_superhost + zipcode + room_type + accommodates + bathrooms + cleaning_fee + minimum_nights + availability_30 + number_of_reviews + log.review_scores_rating + log.review_scores_accuracy + log.review_scores_cleanliness + log.review_scores_checkin + log.review_scores_location + log.review_scores_value + log.reviews_per_month + cancellation_policy 
## 
## ---------------------------------------------------------------------------------------------------
## Variable                         DF       AIC         Sum Sq          RSS        R-Sq     Adj. R-Sq 
## ---------------------------------------------------------------------------------------------------
## number_of_reviews                1     16798.420      1108.099    5379336.276    0.688        0.681 
## log.review_scores_accuracy       1     16799.149      3686.993    5381915.170    0.688        0.681 
## log.review_scores_value          1     16799.432      4688.650    5382916.828    0.687        0.681 
## log.review_scores_checkin        1     16799.953      6535.797    5384763.975    0.687        0.681 
## host_is_superhost                1     16800.747      9348.008    5387576.185    0.687        0.681 
## log.review_scores_location       1     16801.590     12337.853    5390566.030    0.687        0.681 
## log.review_scores_rating         1     16801.799     13077.906    5391306.083    0.687        0.681 
## availability_30                  1     16806.313     29114.348    5407342.525    0.686        0.680 
## log.review_scores_cleanliness    1     16813.249     53842.822    5432070.999    0.685        0.678 
## room_type                        1     16830.565    123316.316    5501544.493    0.681        0.674 
## cleaning_fee                     1     16844.821    167854.107    5546082.285    0.678        0.672 
## log.reviews_per_month            1     16852.364    195445.061    5573673.239    0.676        0.670 
## zipcode                          1     16871.794    341922.035    5720150.213    0.668        0.663 
## minimum_nights                   1     16894.910    353660.437    5731888.614    0.667        0.661 
## bathrooms                        1     16925.543    470347.071    5848575.248    0.660        0.654 
## accommodates                     1     16947.272    554556.763    5932784.940    0.656        0.649 
## cancellation_policy              1     17049.107    990742.327    6368970.504    0.630        0.624 
## ---------------------------------------------------------------------------------------------------
## 
## - number_of_reviews 
## 
## 
##   Step 6 : AIC = 16798.42 
##  price ~ host_is_superhost + zipcode + room_type + accommodates + bathrooms + cleaning_fee + minimum_nights + availability_30 + log.review_scores_rating + log.review_scores_accuracy + log.review_scores_cleanliness + log.review_scores_checkin + log.review_scores_location + log.review_scores_value + log.reviews_per_month + cancellation_policy 
## 
## ---------------------------------------------------------------------------------------------------
## Variable                         DF       AIC         Sum Sq          RSS        R-Sq     Adj. R-Sq 
## ---------------------------------------------------------------------------------------------------
## log.review_scores_accuracy       1     16797.435      3591.190    5382927.466    0.687        0.681 
## log.review_scores_value          1     16797.735      4653.639    5383989.916    0.687        0.681 
## log.review_scores_checkin        1     16798.202      6309.407    5385645.684    0.687        0.681 
## host_is_superhost                1     16799.218      9911.426    5389247.703    0.687        0.681 
## log.review_scores_location       1     16799.817     12035.128    5391371.404    0.687        0.681 
## log.review_scores_rating         1     16800.204     13406.145    5392742.421    0.687        0.681 
## availability_30                  1     16804.510     28705.983    5408042.259    0.686        0.680 
## log.review_scores_cleanliness    1     16811.402     53282.299    5432618.575    0.685        0.678 
## room_type                        1     16828.609    122364.571    5501700.848    0.681        0.675 
## cleaning_fee                     1     16842.835    166797.708    5546133.984    0.678        0.672 
## log.reviews_per_month            1     16862.826    240220.796    5619557.072    0.674        0.667 
## zipcode                          1     16871.286    346431.217    5725767.493    0.668        0.663 
## minimum_nights                   1     16892.911    352555.610    5731891.886    0.667        0.661 
## bathrooms                        1     16924.090    471346.001    5850682.278    0.660        0.654 
## accommodates                     1     16945.444    554120.123    5933456.399    0.656        0.649 
## cancellation_policy              1     17048.143    993974.717    6373310.993    0.630        0.624 
## ---------------------------------------------------------------------------------------------------
## 
## - log.review_scores_accuracy 
## 
## 
##   Step 7 : AIC = 16797.43 
##  price ~ host_is_superhost + zipcode + room_type + accommodates + bathrooms + cleaning_fee + minimum_nights + availability_30 + log.review_scores_rating + log.review_scores_cleanliness + log.review_scores_checkin + log.review_scores_location + log.review_scores_value + log.reviews_per_month + cancellation_policy 
## 
## ----------------------------------------------------------------------------------------------------
## Variable                         DF       AIC         Sum Sq           RSS        R-Sq     Adj. R-Sq 
## ----------------------------------------------------------------------------------------------------
## log.review_scores_value          1     16797.123       5984.112    5388911.579    0.687        0.681 
## log.review_scores_location       1     16797.966       8972.390    5391899.856    0.687        0.681 
## host_is_superhost                1     16798.304      10170.641    5393098.107    0.687        0.681 
## log.review_scores_checkin        1     16798.921      12360.584    5395288.050    0.687        0.681 
## log.review_scores_rating         1     16799.798      15474.638    5398402.104    0.687        0.681 
## availability_30                  1     16803.729      29453.181    5412380.647    0.686        0.680 
## log.review_scores_cleanliness    1     16809.592      50371.415    5433298.881    0.685        0.679 
## room_type                        1     16827.162     120776.634    5503704.100    0.680        0.675 
## cleaning_fee                     1     16841.913     167139.868    5550067.334    0.678        0.672 
## log.reviews_per_month            1     16861.602     239499.685    5622427.151    0.674        0.667 
## zipcode                          1     16871.125     349772.145    5732699.612    0.667        0.663 
## minimum_nights                   1     16891.281     350361.243    5733288.709    0.667        0.661 
## bathrooms                        1     16923.035     471391.906    5854319.372    0.660        0.654 
## accommodates                     1     16944.475     554553.790    5937481.256    0.655        0.649 
## cancellation_policy              1     17048.580    1000611.645    6383539.112    0.629        0.623 
## ----------------------------------------------------------------------------------------------------
## 
## - log.review_scores_value 
## 
## 
##   Step 8 : AIC = 16797.12 
##  price ~ host_is_superhost + zipcode + room_type + accommodates + bathrooms + cleaning_fee + minimum_nights + availability_30 + log.review_scores_rating + log.review_scores_cleanliness + log.review_scores_checkin + log.review_scores_location + log.reviews_per_month + cancellation_policy 
## 
## ----------------------------------------------------------------------------------------------------
## Variable                         DF       AIC         Sum Sq           RSS        R-Sq     Adj. R-Sq 
## ----------------------------------------------------------------------------------------------------
## log.review_scores_location       1     16797.122       7088.365    5395999.944    0.687        0.681 
## host_is_superhost                1     16797.572       8687.262    5397598.840    0.687        0.681 
## log.review_scores_rating         1     16800.062      17538.571    5406450.149    0.686        0.680 
## log.review_scores_checkin        1     16801.145      21390.456    5410302.035    0.686        0.680 
## availability_30                  1     16803.920      31277.536    5420189.115    0.685        0.680 
## log.review_scores_cleanliness    1     16807.666      44651.603    5433563.181    0.685        0.679 
## room_type                        1     16827.657     123835.545    5512747.123    0.680        0.674 
## cleaning_fee                     1     16842.515     170664.520    5559576.098    0.677        0.671 
## log.reviews_per_month            1     16864.366     251164.729    5640076.307    0.673        0.667 
## minimum_nights                   1     16892.104     355034.047    5743945.626    0.667        0.660 
## zipcode                          1     16874.468     363974.745    5752886.324    0.666        0.662 
## bathrooms                        1     16921.234     466176.319    5855087.897    0.660        0.654 
## accommodates                     1     16945.646     560972.180    5949883.758    0.655        0.648 
## cancellation_policy              1     17054.641    1028570.936    6417482.515    0.627        0.621 
## ----------------------------------------------------------------------------------------------------
## 
## - log.review_scores_location 
## 
## 
##   Step 9 : AIC = 16797.12 
##  price ~ host_is_superhost + zipcode + room_type + accommodates + bathrooms + cleaning_fee + minimum_nights + availability_30 + log.review_scores_rating + log.review_scores_cleanliness + log.review_scores_checkin + log.reviews_per_month + cancellation_policy 
## 
## ----------------------------------------------------------------------------------------------------
## Variable                         DF       AIC         Sum Sq           RSS        R-Sq     Adj. R-Sq 
## ----------------------------------------------------------------------------------------------------
## host_is_superhost                1     16797.779       9443.038    5405442.981    0.686        0.681 
## log.review_scores_checkin        1     16799.278      14775.991    5410775.934    0.686        0.680 
## log.review_scores_rating         1     16799.326      14945.111    5410945.054    0.686        0.680 
## availability_30                  1     16803.838      31032.394    5427032.338    0.685        0.679 
## log.review_scores_cleanliness    1     16809.836      52489.721    5448489.665    0.684        0.678 
## room_type                        1     16827.994     125227.301    5521227.245    0.679        0.674 
## cleaning_fee                     1     16842.254     169943.293    5565943.237    0.677        0.671 
## log.reviews_per_month            1     16863.884     249712.375    5645712.318    0.672        0.667 
## minimum_nights                   1     16892.868     358398.760    5754398.704    0.666        0.660 
## zipcode                          1     16878.423     379470.035    5775469.979    0.665        0.661 
## bathrooms                        1     16923.059     473838.546    5869838.490    0.659        0.653 
## accommodates                     1     16944.196     556033.695    5952033.638    0.654        0.648 
## cancellation_policy              1     17054.556    1029573.215    6425573.159    0.627        0.621 
## ----------------------------------------------------------------------------------------------------
## 
## 
## No more variables to be removed.
## 
## Variables Removed: 
## 
## - bed_type 
## - extra_people 
## - host_listings_count 
## - log.review_scores_communication 
## - beds 
## - number_of_reviews 
## - log.review_scores_accuracy 
## - log.review_scores_value 
## - log.review_scores_location 
## 
## 
## Final Model Output 
## ------------------
## 
##                          Model Summary                           
## ----------------------------------------------------------------
## R                       0.829       RMSE                 60.138 
## R-Squared               0.687       Coef. Var            45.750 
## Adj. R-Squared          0.681       MSE                3616.622 
## Pred R-Squared           -Inf       MAE                  39.571 
## ----------------------------------------------------------------
##  RMSE: Root Mean Square Error 
##  MSE: Mean Square Error 
##  MAE: Mean Absolute Error 
## 
##                                    ANOVA                                    
## ---------------------------------------------------------------------------
##                     Sum of                                                 
##                    Squares          DF    Mean Square       F         Sig. 
## ---------------------------------------------------------------------------
## Regression    11828344.256          27     438086.824    121.131    0.0000 
## Residual       5395999.944        1492       3616.622                      
## Total         17224344.200        1519                                     
## ---------------------------------------------------------------------------
## 
##                                                       Parameter Estimates                                                       
## -------------------------------------------------------------------------------------------------------------------------------
##                                          model       Beta    Std. Error    Std. Beta      t        Sig        lower      upper 
## -------------------------------------------------------------------------------------------------------------------------------
##                                    (Intercept)     24.267        10.544                  2.301    0.022       3.584     44.951 
##                             host_is_superhostt      5.920         3.664        0.027     1.616    0.106      -1.266     13.106 
##                                   zipcode28715    -17.741        13.685       -0.022    -1.296    0.195     -44.585      9.103 
##                                   zipcode28732      4.558        14.475        0.005     0.315    0.753     -23.836     32.952 
##                                   zipcode28748    -22.662        60.710       -0.005    -0.373    0.709    -141.748     96.424 
##                                   zipcode28787     45.098        60.955        0.011     0.740    0.460     -74.468    164.664 
##                                   zipcode28801     44.603         8.105        0.176     5.503    0.000      28.705     60.502 
##                                   zipcode28803     23.491         8.359        0.077     2.810    0.005       7.094     39.888 
##                                   zipcode28804     30.290         8.554        0.092     3.541    0.000      13.511     47.069 
##                                   zipcode28805     18.051         8.580        0.055     2.104    0.036       1.221     34.881 
##                                   zipcode28806      5.136         7.783        0.022     0.660    0.509     -10.131     20.402 
##                                   zipcode28815     26.024        60.782        0.006     0.428    0.669     -93.203    145.252 
##                                   zipcode29710     -7.412        60.952       -0.002    -0.122    0.903    -126.973    112.148 
##                          room_typePrivate room    -20.375         3.954       -0.087    -5.154    0.000     -28.130    -12.620 
##                           room_typeShared room    -81.857        23.571       -0.052    -3.473    0.001    -128.093    -35.620 
##                                   accommodates     12.792         1.032        0.284    12.399    0.000      10.768     14.815 
##                                      bathrooms     43.035         3.760        0.256    11.446    0.000      35.660     50.410 
##                                   cleaning_fee      0.311         0.045        0.158     6.855    0.000       0.222      0.400 
##                                 minimum_nights     -2.086         0.210       -0.162    -9.955    0.000      -2.496     -1.675 
##                                availability_30      0.586         0.200        0.044     2.929    0.003       0.194      0.978 
##                       log.review_scores_rating    -25.395        12.493       -0.305    -2.033    0.042     -49.900     -0.890 
##                  log.review_scores_cleanliness    111.975        29.393        0.703     3.810    0.000      54.320    169.630 
##                      log.review_scores_checkin    -66.567        32.933       -0.419    -2.021    0.043    -131.167     -1.967 
##                          log.reviews_per_month    -26.050         3.135       -0.166    -8.309    0.000     -32.199    -19.900 
##                    cancellation_policymoderate      3.225         4.245        0.015     0.760    0.448      -5.103     11.552 
## cancellation_policystrict_14_with_grace_period     12.178         4.630        0.053     2.630    0.009       3.097     21.260 
##             cancellation_policysuper_strict_30      5.536        15.351        0.006     0.361    0.718     -24.576     35.648 
##             cancellation_policysuper_strict_60    210.840        12.915        0.271    16.325    0.000     185.506    236.174 
## -------------------------------------------------------------------------------------------------------------------------------
final.main.model <- lm(price ~ host_is_superhost
+ zipcode
+ room_type
+ accommodates
+ bathrooms
+ cleaning_fee
+ minimum_nights
+ availability_30
+ review_scores_cleanliness
+ review_scores_checkin
+ review_scores_location
+ review_scores_value
+ reviews_per_month
+ cancellation_policy, data=train.airbnb)
kable(tidy(final.main.model), digits=3)
term estimate std.error statistic p.value
(Intercept) 23.755 10.637 2.233 0.026
host_is_superhostt 2.753 3.677 0.749 0.454
zipcode28715 -19.840 13.805 -1.437 0.151
zipcode28732 2.895 14.594 0.198 0.843
zipcode28748 -28.538 61.201 -0.466 0.641
zipcode28787 40.901 61.578 0.664 0.507
zipcode28801 39.916 8.264 4.830 0.000
zipcode28803 21.366 8.449 2.529 0.012
zipcode28804 27.466 8.644 3.178 0.002
zipcode28805 14.894 8.684 1.715 0.087
zipcode28806 2.323 7.862 0.296 0.768
zipcode28815 34.707 61.244 0.567 0.571
zipcode29710 -6.194 61.439 -0.101 0.920
room_typePrivate room -18.525 3.976 -4.659 0.000
room_typeShared room -81.884 23.785 -3.443 0.001
accommodates 12.651 1.041 12.152 0.000
bathrooms 44.178 3.799 11.628 0.000
cleaning_fee 0.311 0.046 6.784 0.000
minimum_nights -1.921 0.208 -9.227 0.000
availability_30 0.462 0.201 2.295 0.022
review_scores_cleanliness 13.436 3.794 3.542 0.000
review_scores_checkin -13.548 4.825 -2.808 0.005
review_scores_location 5.638 4.049 1.392 0.164
review_scores_value -7.784 3.938 -1.977 0.048
reviews_per_month -4.461 0.697 -6.403 0.000
cancellation_policymoderate 3.310 4.287 0.772 0.440
cancellation_policystrict_14_with_grace_period 12.669 4.680 2.707 0.007
cancellation_policysuper_strict_30 8.309 15.512 0.536 0.592
cancellation_policysuper_strict_60 216.418 13.023 16.618 0.000
#model with interaction effects
interactions.model <- lm(price ~ cleaning_fee * bathrooms + cleaning_fee * accommodates + room_type * bathrooms + accommodates * bathrooms + cleaning_fee * review_scores_cleanliness + zipcode * review_scores_location + availability_30 * minimum_nights + cancellation_policy * accommodates + host_is_superhost
+ host_listings_count
+ zipcode
+ room_type
+ accommodates
+ bathrooms
+ beds
+ bed_type
+ cleaning_fee
+ extra_people
+ minimum_nights
+ availability_30
+ number_of_reviews
+ review_scores_rating
+ review_scores_accuracy
+ review_scores_cleanliness
+ review_scores_checkin
+ review_scores_communication
+ review_scores_location
+ review_scores_value
+ reviews_per_month
+ cancellation_policy, data=train.airbnb)

#anova test
kable(anova(full.model, interactions.model))
Res.Df RSS Df Sum of Sq F Pr(>F)
1480 5373756 NA NA NA NA
1462 4920903 18 452852.8 7.474586 0
backwards.model.2 <- ols_step_backward_aic(interactions.model, details=TRUE)
## Backward Elimination Method 
## ---------------------------
## 
## Candidate Terms: 
## 
## 1 . cleaning_fee 
## 2 . bathrooms 
## 3 . accommodates 
## 4 . room_type 
## 5 . review_scores_cleanliness 
## 6 . zipcode 
## 7 . review_scores_location 
## 8 . availability_30 
## 9 . minimum_nights 
## 10 . cancellation_policy 
## 11 . host_is_superhost 
## 12 . host_listings_count 
## 13 . beds 
## 14 . bed_type 
## 15 . extra_people 
## 16 . number_of_reviews 
## 17 . review_scores_rating 
## 18 . review_scores_accuracy 
## 19 . review_scores_checkin 
## 20 . review_scores_communication 
## 21 . review_scores_value 
## 22 . reviews_per_month 
## 23 . cleaning_fee:bathrooms 
## 24 . cleaning_fee:accommodates 
## 25 . bathrooms:room_type 
## 26 . bathrooms:accommodates 
## 27 . cleaning_fee:review_scores_cleanliness 
## 28 . zipcode:review_scores_location 
## 29 . availability_30:minimum_nights 
## 30 . accommodates:cancellation_policy 
## 
##  Step 0: AIC = 16725.03 
##  price ~ cleaning_fee + bathrooms + accommodates + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + host_is_superhost + host_listings_count + beds + bed_type + extra_people + number_of_reviews + review_scores_rating + review_scores_accuracy + review_scores_checkin + review_scores_communication + review_scores_value + reviews_per_month + cleaning_fee:bathrooms + cleaning_fee:accommodates + bathrooms:room_type + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + availability_30:minimum_nights + accommodates:cancellation_policy 
## 
## ------------------------------------------------------------------------------------------------------------
## Variable                                  DF       AIC         Sum Sq          RSS        R-Sq     Adj. R-Sq 
## ------------------------------------------------------------------------------------------------------------
## review_scores_location                    1     16725.029         0.000    4920903.151    0.714        0.703 
## review_scores_rating                      1     16723.030         3.478    4920906.629    0.714        0.703 
## beds                                      1     16723.069       129.051    4921032.202    0.714        0.703 
## review_scores_accuracy                    1     16723.070       132.798    4921035.949    0.714        0.703 
## host_listings_count                       1     16723.137       349.056    4921252.207    0.714        0.703 
## review_scores_communication               1     16723.226       636.520    4921539.671    0.714        0.703 
## extra_people                              1     16723.649      2006.550    4922909.701    0.714        0.703 
## accommodates                              1     16723.882      2760.120    4923663.271    0.714        0.703 
## number_of_reviews                         1     16723.966      3033.483    4923936.634    0.714        0.703 
## cleaning_fee:bathrooms                    1     16724.076      3389.448    4924292.598    0.714        0.703 
## host_is_superhost                         1     16724.355      4292.235    4925195.386    0.714        0.703 
## availability_30:minimum_nights            1     16724.358      4303.918    4925207.069    0.714        0.703 
## cleaning_fee:accommodates                 1     16724.663      5291.917    4926195.068    0.714        0.703 
## review_scores_checkin                     1     16724.859      5926.783    4926829.934    0.714        0.703 
## room_type                                 1     16722.962      6260.770    4927163.920    0.714        0.703 
## bathrooms:room_type                       1     16723.006      6402.976    4927306.127    0.714        0.703 
## bed_type                                  1     16719.329      7451.048    4928354.199    0.714        0.704 
## bathrooms                                 1     16725.552      8171.861    4929075.012    0.714        0.703 
## review_scores_value                       1     16725.831      9077.318    4929980.469    0.714        0.703 
## availability_30                           1     16726.803     12231.641    4933134.791    0.714        0.703 
## cleaning_fee:review_scores_cleanliness    1     16732.978     32314.710    4953217.861    0.712        0.701 
## cleaning_fee                              1     16734.603     37612.341    4958515.492    0.712        0.701 
## cancellation_policy                       1     16729.802     41525.536    4962428.686    0.712        0.701 
## review_scores_cleanliness                 1     16736.338     43276.260    4964179.410    0.712        0.701 
## bathrooms:accommodates                    1     16738.645     50813.514    4971716.664    0.711        0.700 
## zipcode:review_scores_location            1     16729.919     87829.147    5008732.297    0.709        0.699 
## zipcode                                   1     16731.535     93155.860    5014059.011    0.709        0.699 
## reviews_per_month                         1     16765.245    138586.048    5059489.199    0.706        0.695 
## accommodates:cancellation_policy          1     16761.517    146154.290    5067057.441    0.706        0.695 
## minimum_nights                            1     16774.474    169399.693    5090302.844    0.704        0.693 
## ------------------------------------------------------------------------------------------------------------
## 
## 
## - bed_type 
## 
## 
##   Step 1 : AIC = 16719.33 
##  price ~ cleaning_fee + bathrooms + accommodates + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + host_is_superhost + host_listings_count + beds + extra_people + number_of_reviews + review_scores_rating + review_scores_accuracy + review_scores_checkin + review_scores_communication + review_scores_value + reviews_per_month + cleaning_fee:bathrooms + cleaning_fee:accommodates + bathrooms:room_type + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + availability_30:minimum_nights + accommodates:cancellation_policy 
## 
## ------------------------------------------------------------------------------------------------------------
## Variable                                  DF       AIC         Sum Sq          RSS        R-Sq     Adj. R-Sq 
## ------------------------------------------------------------------------------------------------------------
## review_scores_location                    1     16719.329         0.000    4928354.199    0.714        0.704 
## review_scores_rating                      1     16717.331         4.844    4928359.043    0.714        0.704 
## beds                                      1     16717.363       109.083    4928463.282    0.714        0.704 
## review_scores_accuracy                    1     16717.392       204.763    4928558.961    0.714        0.704 
## host_listings_count                       1     16717.428       320.589    4928674.788    0.714        0.704 
## review_scores_communication               1     16717.518       612.105    4928966.304    0.714        0.704 
## extra_people                              1     16717.955      2029.507    4930383.706    0.714        0.704 
## accommodates                              1     16718.259      3015.143    4931369.342    0.714        0.704 
## number_of_reviews                         1     16718.288      3108.441    4931462.640    0.714        0.704 
## cleaning_fee:bathrooms                    1     16718.328      3238.549    4931592.747    0.714        0.704 
## host_is_superhost                         1     16718.655      4301.136    4932655.334    0.714        0.703 
## availability_30:minimum_nights            1     16718.757      4630.369    4932984.568    0.714        0.703 
## cleaning_fee:accommodates                 1     16718.975      5338.652    4933692.851    0.714        0.703 
## review_scores_checkin                     1     16719.099      5740.974    4934095.173    0.714        0.703 
## bathrooms:room_type                       1     16717.255      6249.655    4934603.854    0.714        0.704 
## room_type                                 1     16717.302      6401.776    4934755.975    0.714        0.704 
## bathrooms                                 1     16719.776      7939.746    4936293.945    0.713        0.703 
## review_scores_value                       1     16720.080      8925.616    4937279.815    0.713        0.703 
## availability_30                           1     16721.183     12512.728    4940866.927    0.713        0.703 
## cleaning_fee:review_scores_cleanliness    1     16727.438     32885.905    4961240.103    0.712        0.702 
## cleaning_fee                              1     16729.250     38804.770    4967158.969    0.712        0.701 
## cancellation_policy                       1     16724.007     41278.905    4969633.104    0.711        0.702 
## review_scores_cleanliness                 1     16730.672     43451.771    4971805.969    0.711        0.701 
## bathrooms:accommodates                    1     16733.086     51355.263    4979709.462    0.711        0.701 
## zipcode:review_scores_location            1     16724.341     88364.708    5016718.907    0.709        0.700 
## zipcode                                   1     16725.510     92224.786    5020578.984    0.709        0.700 
## reviews_per_month                         1     16759.714    139358.949    5067713.148    0.706        0.695 
## accommodates:cancellation_policy          1     16755.188    144277.909    5072632.108    0.705        0.696 
## minimum_nights                            1     16768.563    168950.160    5097304.359    0.704        0.694 
## ------------------------------------------------------------------------------------------------------------
## 
## - bathrooms:room_type 
## 
## 
##   Step 2 : AIC = 16717.26 
##  price ~ cleaning_fee + bathrooms + accommodates + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + host_is_superhost + host_listings_count + beds + extra_people + number_of_reviews + review_scores_rating + review_scores_accuracy + review_scores_checkin + review_scores_communication + review_scores_value + reviews_per_month + cleaning_fee:bathrooms + cleaning_fee:accommodates + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + availability_30:minimum_nights + accommodates:cancellation_policy 
## 
## ------------------------------------------------------------------------------------------------------------
## Variable                                  DF       AIC         Sum Sq          RSS        R-Sq     Adj. R-Sq 
## ------------------------------------------------------------------------------------------------------------
## review_scores_location                    1     16717.255         0.000    4934603.854    0.714        0.704 
## review_scores_rating                      1     16715.256         3.075    4934606.929    0.714        0.704 
## beds                                      1     16715.277        68.285    4934672.139    0.714        0.704 
## review_scores_accuracy                    1     16715.291       114.026    4934717.880    0.714        0.704 
## host_listings_count                       1     16715.400       468.291    4935072.145    0.713        0.704 
## review_scores_communication               1     16715.430       566.528    4935170.382    0.713        0.704 
## extra_people                              1     16715.906      2110.710    4936714.564    0.713        0.704 
## accommodates                              1     16716.022      2487.703    4937091.557    0.713        0.704 
## number_of_reviews                         1     16716.079      2673.477    4937277.331    0.713        0.704 
## bathrooms                                 1     16716.292      3364.618    4937968.472    0.713        0.704 
## host_is_superhost                         1     16716.632      4472.096    4939075.950    0.713        0.703 
## availability_30:minimum_nights            1     16716.718      4751.428    4939355.282    0.713        0.703 
## cleaning_fee:bathrooms                    1     16716.805      5032.551    4939636.405    0.713        0.703 
## review_scores_checkin                     1     16717.119      6054.855    4940658.709    0.713        0.703 
## review_scores_value                       1     16718.015      8966.030    4943569.884    0.713        0.703 
## cleaning_fee:accommodates                 1     16718.018      8975.534    4943579.388    0.713        0.703 
## availability_30                           1     16718.637     10988.861    4945592.715    0.713        0.703 
## cleaning_fee:review_scores_cleanliness    1     16724.851     31249.592    4965853.446    0.712        0.702 
## cleaning_fee                              1     16727.377     39509.573    4974113.427    0.711        0.701 
## cancellation_policy                       1     16722.058     41739.788    4976343.642    0.711        0.702 
## review_scores_cleanliness                 1     16728.296     42517.311    4977121.165    0.711        0.701 
## bathrooms:accommodates                    1     16736.453     69298.471    5003902.325    0.709        0.700 
## zipcode:review_scores_location            1     16722.238     88380.203    5022984.057    0.708        0.700 
## zipcode                                   1     16724.443     95671.653    5030275.507    0.708        0.699 
## reviews_per_month                         1     16758.599    142737.952    5077341.806    0.705        0.695 
## accommodates:cancellation_policy          1     16752.822    143483.613    5078087.467    0.705        0.696 
## room_type                                 1     16760.276    155033.816    5089637.670    0.705        0.695 
## minimum_nights                            1     16766.926    170628.472    5105232.326    0.704        0.694 
## ------------------------------------------------------------------------------------------------------------
## 
## - review_scores_rating 
## 
## 
##   Step 3 : AIC = 16715.26 
##  price ~ cleaning_fee + bathrooms + accommodates + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + host_is_superhost + host_listings_count + beds + extra_people + number_of_reviews + review_scores_accuracy + review_scores_checkin + review_scores_communication + review_scores_value + reviews_per_month + cleaning_fee:bathrooms + cleaning_fee:accommodates + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + availability_30:minimum_nights + accommodates:cancellation_policy 
## 
## ------------------------------------------------------------------------------------------------------------
## Variable                                  DF       AIC         Sum Sq          RSS        R-Sq     Adj. R-Sq 
## ------------------------------------------------------------------------------------------------------------
## review_scores_location                    1     16715.256         0.000    4934606.929    0.714        0.704 
## beds                                      1     16713.278        68.432    4934675.361    0.714        0.704 
## review_scores_accuracy                    1     16713.291       110.952    4934717.881    0.714        0.704 
## host_listings_count                       1     16713.400       465.458    4935072.388    0.713        0.704 
## review_scores_communication               1     16713.432       571.147    4935178.076    0.713        0.704 
## extra_people                              1     16713.907      2112.374    4936719.304    0.713        0.704 
## accommodates                              1     16714.022      2484.654    4937091.583    0.713        0.704 
## number_of_reviews                         1     16714.094      2719.222    4937326.151    0.713        0.704 
## bathrooms                                 1     16714.293      3367.192    4937974.121    0.713        0.704 
## host_is_superhost                         1     16714.640      4495.181    4939102.110    0.713        0.704 
## availability_30:minimum_nights            1     16714.724      4766.362    4939373.292    0.713        0.704 
## cleaning_fee:bathrooms                    1     16714.805      5030.604    4939637.533    0.713        0.704 
## review_scores_checkin                     1     16715.123      6064.188    4940671.118    0.713        0.704 
## cleaning_fee:accommodates                 1     16716.018      8974.259    4943581.188    0.713        0.703 
## review_scores_value                       1     16716.198      9557.271    4944164.200    0.713        0.703 
## availability_30                           1     16716.637     10985.799    4945592.728    0.713        0.703 
## cleaning_fee:review_scores_cleanliness    1     16722.879     31338.466    4965945.395    0.712        0.702 
## cleaning_fee                              1     16725.439     39709.597    4974316.527    0.711        0.702 
## cancellation_policy                       1     16720.070     41774.174    4976381.104    0.711        0.702 
## review_scores_cleanliness                 1     16727.675     47031.830    4981638.759    0.711        0.701 
## bathrooms:accommodates                    1     16734.479     69381.296    5003988.226    0.709        0.700 
## zipcode:review_scores_location            1     16720.257     88439.998    5023046.928    0.708        0.700 
## zipcode                                   1     16722.445     95675.625    5030282.554    0.708        0.700 
## reviews_per_month                         1     16756.653    142915.685    5077522.615    0.705        0.695 
## accommodates:cancellation_policy          1     16750.915    143792.114    5078399.044    0.705        0.696 
## room_type                                 1     16758.310    155144.919    5089751.848    0.705        0.695 
## minimum_nights                            1     16765.456    172406.097    5107013.026    0.704        0.694 
## ------------------------------------------------------------------------------------------------------------
## 
## - beds 
## 
## 
##   Step 4 : AIC = 16713.28 
##  price ~ cleaning_fee + bathrooms + accommodates + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + host_is_superhost + host_listings_count + extra_people + number_of_reviews + review_scores_accuracy + review_scores_checkin + review_scores_communication + review_scores_value + reviews_per_month + cleaning_fee:bathrooms + cleaning_fee:accommodates + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + availability_30:minimum_nights + accommodates:cancellation_policy 
## 
## ------------------------------------------------------------------------------------------------------------
## Variable                                  DF       AIC         Sum Sq          RSS        R-Sq     Adj. R-Sq 
## ------------------------------------------------------------------------------------------------------------
## review_scores_location                    1     16713.278         0.000    4934675.361    0.714        0.704 
## review_scores_accuracy                    1     16711.311       108.516    4934783.877    0.713        0.704 
## host_listings_count                       1     16711.407       420.071    4935095.433    0.713        0.704 
## review_scores_communication               1     16711.458       585.155    4935260.516    0.713        0.704 
## extra_people                              1     16711.923      2097.448    4936772.809    0.713        0.704 
## number_of_reviews                         1     16712.123      2744.849    4937420.210    0.713        0.704 
## accommodates                              1     16712.280      3255.068    4937930.430    0.713        0.704 
## bathrooms                                 1     16712.324      3397.781    4938073.143    0.713        0.704 
## host_is_superhost                         1     16712.668      4516.119    4939191.481    0.713        0.704 
## availability_30:minimum_nights            1     16712.744      4763.115    4939438.476    0.713        0.704 
## cleaning_fee:bathrooms                    1     16712.830      5043.928    4939719.289    0.713        0.704 
## review_scores_checkin                     1     16713.134      6032.310    4940707.671    0.713        0.704 
## cleaning_fee:accommodates                 1     16714.022      8917.630    4943592.992    0.713        0.704 
## review_scores_value                       1     16714.222      9567.988    4944243.350    0.713        0.704 
## availability_30                           1     16714.647     10949.583    4945624.944    0.713        0.704 
## cleaning_fee:review_scores_cleanliness    1     16720.919     31399.668    4966075.029    0.712        0.702 
## cleaning_fee                              1     16723.451     39681.104    4974356.466    0.711        0.702 
## cancellation_policy                       1     16718.195     42114.433    4976789.794    0.711        0.702 
## review_scores_cleanliness                 1     16725.684     46993.084    4981668.445    0.711        0.701 
## bathrooms:accommodates                    1     16732.514     69428.738    5004104.099    0.709        0.700 
## zipcode:review_scores_location            1     16718.358     88704.945    5023380.306    0.708        0.700 
## zipcode                                   1     16720.602     96125.227    5030800.589    0.708        0.700 
## reviews_per_month                         1     16754.673    142914.439    5077589.801    0.705        0.696 
## accommodates:cancellation_policy          1     16749.884    146959.128    5081634.489    0.705        0.696 
## room_type                                 1     16756.319    155108.608    5089783.969    0.705        0.695 
## minimum_nights                            1     16763.549    172649.681    5107325.043    0.703        0.694 
## ------------------------------------------------------------------------------------------------------------
## 
## - review_scores_accuracy 
## 
## 
##   Step 5 : AIC = 16711.31 
##  price ~ cleaning_fee + bathrooms + accommodates + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + host_is_superhost + host_listings_count + extra_people + number_of_reviews + review_scores_checkin + review_scores_communication + review_scores_value + reviews_per_month + cleaning_fee:bathrooms + cleaning_fee:accommodates + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + availability_30:minimum_nights + accommodates:cancellation_policy 
## 
## ------------------------------------------------------------------------------------------------------------
## Variable                                  DF       AIC         Sum Sq          RSS        R-Sq     Adj. R-Sq 
## ------------------------------------------------------------------------------------------------------------
## review_scores_location                    1     16711.311         0.000    4934783.877    0.713        0.704 
## host_listings_count                       1     16709.442       423.991    4935207.868    0.713        0.704 
## review_scores_communication               1     16709.561       811.925    4935595.802    0.713        0.704 
## extra_people                              1     16709.948      2069.643    4936853.520    0.713        0.704 
## number_of_reviews                         1     16710.160      2757.926    4937541.803    0.713        0.704 
## accommodates                              1     16710.304      3225.430    4938009.307    0.713        0.704 
## bathrooms                                 1     16710.366      3426.112    4938209.988    0.713        0.704 
## host_is_superhost                         1     16710.714      4555.858    4939339.735    0.713        0.704 
## availability_30:minimum_nights            1     16710.768      4731.547    4939515.424    0.713        0.704 
## cleaning_fee:bathrooms                    1     16710.852      5006.445    4939790.322    0.713        0.704 
## review_scores_checkin                     1     16711.324      6538.411    4941322.288    0.713        0.704 
## cleaning_fee:accommodates                 1     16712.040      8866.683    4943650.560    0.713        0.704 
## review_scores_value                       1     16712.415     10087.752    4944871.629    0.713        0.704 
## availability_30                           1     16712.711     11051.623    4945835.500    0.713        0.704 
## cleaning_fee:review_scores_cleanliness    1     16718.945     31376.027    4966159.903    0.712        0.702 
## cleaning_fee                              1     16721.478     39659.795    4974443.672    0.711        0.702 
## cancellation_policy                       1     16716.200     42024.718    4976808.595    0.711        0.702 
## review_scores_cleanliness                 1     16724.578     49816.322    4984600.199    0.711        0.701 
## bathrooms:accommodates                    1     16730.540     69404.369    5004188.246    0.709        0.700 
## zipcode:review_scores_location            1     16716.447     88891.199    5023675.075    0.708        0.700 
## zipcode                                   1     16718.688     96303.339    5031087.215    0.708        0.700 
## reviews_per_month                         1     16752.691    142864.648    5077648.524    0.705        0.696 
## accommodates:cancellation_policy          1     16748.212    147949.501    5082733.378    0.705        0.696 
## room_type                                 1     16754.333    155046.651    5089830.528    0.704        0.695 
## minimum_nights                            1     16761.561    172581.481    5107365.358    0.703        0.694 
## ------------------------------------------------------------------------------------------------------------
## 
## - host_listings_count 
## 
## 
##   Step 6 : AIC = 16709.44 
##  price ~ cleaning_fee + bathrooms + accommodates + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + host_is_superhost + extra_people + number_of_reviews + review_scores_checkin + review_scores_communication + review_scores_value + reviews_per_month + cleaning_fee:bathrooms + cleaning_fee:accommodates + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + availability_30:minimum_nights + accommodates:cancellation_policy 
## 
## ------------------------------------------------------------------------------------------------------------
## Variable                                  DF       AIC         Sum Sq          RSS        R-Sq     Adj. R-Sq 
## ------------------------------------------------------------------------------------------------------------
## review_scores_location                    1     16709.442         0.000    4935207.868    0.713        0.704 
## review_scores_communication               1     16707.736       955.252    4936163.119    0.713        0.704 
## extra_people                              1     16708.044      1956.957    4937164.825    0.713        0.704 
## number_of_reviews                         1     16708.291      2759.319    4937967.186    0.713        0.704 
## accommodates                              1     16708.395      3095.473    4938303.341    0.713        0.704 
## bathrooms                                 1     16708.573      3676.392    4938884.259    0.713        0.704 
## host_is_superhost                         1     16708.798      4406.497    4939614.364    0.713        0.704 
## cleaning_fee:bathrooms                    1     16708.878      4666.521    4939874.389    0.713        0.704 
## availability_30:minimum_nights            1     16708.882      4680.712    4939888.579    0.713        0.704 
## review_scores_checkin                     1     16709.416      6415.219    4941623.086    0.713        0.704 
## cleaning_fee:accommodates                 1     16710.042      8449.295    4943657.163    0.713        0.704 
## review_scores_value                       1     16710.520     10004.754    4945212.621    0.713        0.704 
## availability_30                           1     16710.856     11099.430    4946307.297    0.713        0.704 
## cleaning_fee:review_scores_cleanliness    1     16718.257     35242.342    4970450.210    0.711        0.702 
## cleaning_fee                              1     16721.054     44396.442    4979604.309    0.711        0.702 
## cancellation_policy                       1     16716.122     47896.238    4983104.105    0.711        0.702 
## review_scores_cleanliness                 1     16722.773     50032.261    4985240.129    0.711        0.702 
## bathrooms:accommodates                    1     16728.560     69046.941    5004254.809    0.709        0.700 
## zipcode:review_scores_location            1     16714.673     89214.523    5024422.390    0.708        0.700 
## zipcode                                   1     16716.697     95906.845    5031114.713    0.708        0.700 
## reviews_per_month                         1     16750.748    142632.581    5077840.448    0.705        0.696 
## accommodates:cancellation_policy          1     16746.213    147526.854    5082734.722    0.705        0.696 
## room_type                                 1     16752.443    154989.855    5090197.723    0.704        0.695 
## minimum_nights                            1     16759.996    173622.063    5108829.930    0.703        0.694 
## ------------------------------------------------------------------------------------------------------------
## 
## - review_scores_communication 
## 
## 
##   Step 7 : AIC = 16707.74 
##  price ~ cleaning_fee + bathrooms + accommodates + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + host_is_superhost + extra_people + number_of_reviews + review_scores_checkin + review_scores_value + reviews_per_month + cleaning_fee:bathrooms + cleaning_fee:accommodates + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + availability_30:minimum_nights + accommodates:cancellation_policy 
## 
## ------------------------------------------------------------------------------------------------------------
## Variable                                  DF       AIC         Sum Sq          RSS        R-Sq     Adj. R-Sq 
## ------------------------------------------------------------------------------------------------------------
## review_scores_location                    1     16707.736         0.000    4936163.119    0.713        0.704 
## extra_people                              1     16706.326      1917.404    4938080.523    0.713        0.705 
## number_of_reviews                         1     16706.610      2841.531    4939004.650    0.713        0.705 
## accommodates                              1     16706.685      3082.217    4939245.337    0.713        0.704 
## bathrooms                                 1     16706.871      3688.414    4939851.534    0.713        0.704 
## host_is_superhost                         1     16707.076      4353.826    4940516.945    0.713        0.704 
## cleaning_fee:bathrooms                    1     16707.151      4597.638    4940760.758    0.713        0.704 
## availability_30:minimum_nights            1     16707.171      4662.123    4940825.243    0.713        0.704 
## cleaning_fee:accommodates                 1     16708.267      8226.236    4944389.355    0.713        0.704 
## review_scores_value                       1     16709.096     10924.378    4947087.497    0.713        0.704 
## availability_30                           1     16709.224     11340.328    4947503.448    0.713        0.704 
## review_scores_checkin                     1     16711.323     18177.539    4954340.659    0.712        0.704 
## cleaning_fee:review_scores_cleanliness    1     16716.500     35081.835    4971244.955    0.711        0.703 
## cleaning_fee                              1     16719.253     44092.876    4980255.996    0.711        0.702 
## cancellation_policy                       1     16714.342     47660.843    4983823.963    0.711        0.702 
## review_scores_cleanliness                 1     16720.789     49128.803    4985291.922    0.711        0.702 
## bathrooms:accommodates                    1     16726.794     68862.513    5005025.632    0.709        0.701 
## zipcode:review_scores_location            1     16712.826     88763.050    5024926.169    0.708        0.701 
## zipcode                                   1     16714.960     95822.515    5031985.634    0.708        0.700 
## reviews_per_month                         1     16748.960    142383.408    5078546.527    0.705        0.696 
## accommodates:cancellation_policy          1     16745.230    149975.947    5086139.067    0.705        0.696 
## room_type                                 1     16750.648    154720.267    5090883.387    0.704        0.696 
## minimum_nights                            1     16758.270    173586.333    5109749.453    0.703        0.694 
## ------------------------------------------------------------------------------------------------------------
## 
## - extra_people 
## 
## 
##   Step 8 : AIC = 16706.33 
##  price ~ cleaning_fee + bathrooms + accommodates + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + host_is_superhost + number_of_reviews + review_scores_checkin + review_scores_value + reviews_per_month + cleaning_fee:bathrooms + cleaning_fee:accommodates + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + availability_30:minimum_nights + accommodates:cancellation_policy 
## 
## ------------------------------------------------------------------------------------------------------------
## Variable                                  DF       AIC         Sum Sq          RSS        R-Sq     Adj. R-Sq 
## ------------------------------------------------------------------------------------------------------------
## review_scores_location                    1     16706.326         0.000    4938080.523    0.713        0.705 
## number_of_reviews                         1     16705.154      2691.496    4940772.019    0.713        0.705 
## accommodates                              1     16705.335      3280.074    4941360.597    0.713        0.705 
## bathrooms                                 1     16705.418      3549.729    4941630.252    0.713        0.705 
## cleaning_fee:bathrooms                    1     16705.721      4535.572    4942616.095    0.713        0.704 
## host_is_superhost                         1     16705.760      4661.235    4942741.758    0.713        0.704 
## availability_30:minimum_nights            1     16705.801      4794.636    4942875.159    0.713        0.704 
## cleaning_fee:accommodates                 1     16707.028      8786.670    4946867.193    0.713        0.704 
## review_scores_value                       1     16707.735     11086.841    4949167.364    0.713        0.704 
## availability_30                           1     16707.916     11676.036    4949756.559    0.713        0.704 
## review_scores_checkin                     1     16709.926     18226.461    4956306.984    0.712        0.704 
## cleaning_fee:review_scores_cleanliness    1     16714.948     34629.887    4972710.410    0.711        0.703 
## cleaning_fee                              1     16718.333     45715.741    4983796.264    0.711        0.702 
## cancellation_policy                       1     16712.759     47113.551    4985194.074    0.711        0.703 
## review_scores_cleanliness                 1     16719.323     48962.441    4987042.964    0.710        0.702 
## bathrooms:accommodates                    1     16725.410     68972.191    5007052.714    0.709        0.701 
## zipcode:review_scores_location            1     16711.465     88959.076    5027039.599    0.708        0.701 
## zipcode                                   1     16713.613     96067.719    5034148.242    0.708        0.700 
## reviews_per_month                         1     16747.951    143778.414    5081858.937    0.705        0.696 
## accommodates:cancellation_policy          1     16744.019    150699.227    5088779.750    0.705        0.696 
## room_type                                 1     16748.712    153020.114    5091100.637    0.704        0.696 
## minimum_nights                            1     16757.335    175249.457    5113329.980    0.703        0.694 
## ------------------------------------------------------------------------------------------------------------
## 
## - number_of_reviews 
## 
## 
##   Step 9 : AIC = 16705.15 
##  price ~ cleaning_fee + bathrooms + accommodates + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + host_is_superhost + review_scores_checkin + review_scores_value + reviews_per_month + cleaning_fee:bathrooms + cleaning_fee:accommodates + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + availability_30:minimum_nights + accommodates:cancellation_policy 
## 
## ------------------------------------------------------------------------------------------------------------
## Variable                                  DF       AIC         Sum Sq          RSS        R-Sq     Adj. R-Sq 
## ------------------------------------------------------------------------------------------------------------
## review_scores_location                    1     16705.154         0.000    4940772.019    0.713        0.705 
## accommodates                              1     16704.147      3228.415    4944000.434    0.713        0.705 
## bathrooms                                 1     16704.270      3628.882    4944400.901    0.713        0.705 
## host_is_superhost                         1     16704.363      3931.356    4944703.375    0.713        0.705 
## cleaning_fee:bathrooms                    1     16704.570      4603.513    4945375.532    0.713        0.705 
## availability_30:minimum_nights            1     16704.641      4835.635    4945607.654    0.713        0.705 
## cleaning_fee:accommodates                 1     16705.931      9034.802    4949806.821    0.713        0.704 
## review_scores_value                       1     16706.637     11333.649    4952105.668    0.712        0.704 
## availability_30                           1     16706.726     11623.561    4952395.580    0.712        0.704 
## review_scores_checkin                     1     16709.003     19049.343    4959821.362    0.712        0.704 
## cleaning_fee:review_scores_cleanliness    1     16713.635     34186.803    4974958.823    0.711        0.703 
## cleaning_fee                              1     16717.296     46180.788    4986952.807    0.710        0.702 
## cancellation_policy                       1     16711.883     48107.043    4988879.062    0.710        0.703 
## review_scores_cleanliness                 1     16718.438     49928.982    4990701.001    0.710        0.702 
## bathrooms:accommodates                    1     16724.096     68541.671    5009313.690    0.709        0.701 
## zipcode:review_scores_location            1     16710.061     88239.895    5029011.914    0.708        0.701 
## zipcode                                   1     16712.395     95967.034    5036739.054    0.708        0.700 
## accommodates:cancellation_policy          1     16742.736    150408.246    5091180.265    0.704        0.696 
## room_type                                 1     16748.031    154746.032    5095518.051    0.704        0.696 
## minimum_nights                            1     16756.481    176413.966    5117185.986    0.703        0.694 
## reviews_per_month                         1     16767.916    215055.913    5155827.933    0.701        0.692 
## ------------------------------------------------------------------------------------------------------------
## 
## - accommodates 
## 
## 
##   Step 10 : AIC = 16704.15 
##  price ~ cleaning_fee + bathrooms + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + host_is_superhost + review_scores_checkin + review_scores_value + reviews_per_month + cleaning_fee:bathrooms + cleaning_fee:accommodates + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + availability_30:minimum_nights + accommodates:cancellation_policy 
## 
## ------------------------------------------------------------------------------------------------------------
## Variable                                  DF       AIC         Sum Sq          RSS        R-Sq     Adj. R-Sq 
## ------------------------------------------------------------------------------------------------------------
## review_scores_location                    1     16704.147         0.000    4944000.434    0.713        0.705 
## cleaning_fee:bathrooms                    1     16702.859      2315.105    4946315.539    0.713        0.705 
## bathrooms                                 1     16703.019      2837.386    4946837.820    0.713        0.705 
## host_is_superhost                         1     16703.335      3865.174    4947865.608    0.713        0.705 
## availability_30:minimum_nights            1     16703.738      5177.331    4949177.765    0.713        0.704 
## cleaning_fee:accommodates                 1     16704.707      8333.452    4952333.886    0.712        0.704 
## review_scores_value                       1     16705.352     10433.840    4954434.274    0.712        0.704 
## availability_30                           1     16705.731     11671.216    4955671.650    0.712        0.704 
## review_scores_checkin                     1     16707.770     18324.058    4962324.492    0.712        0.704 
## cleaning_fee:review_scores_cleanliness    1     16712.958     35288.615    4979289.049    0.711        0.703 
## review_scores_cleanliness                 1     16716.825     47971.835    4991972.269    0.710        0.702 
## cancellation_policy                       1     16711.831     51279.177    4995279.611    0.710        0.702 
## cleaning_fee                              1     16720.986     61655.711    5005656.145    0.709        0.701 
## zipcode:review_scores_location            1     16709.180     88713.536    5032713.970    0.708        0.701 
## zipcode                                   1     16711.498     96394.849    5040395.283    0.707        0.700 
## bathrooms:accommodates                    1     16736.829    114103.333    5058103.767    0.706        0.698 
## room_type                                 1     16751.264    169089.927    5113090.361    0.703        0.695 
## accommodates:cancellation_policy          1     16749.519    176681.469    5120681.903    0.703        0.695 
## minimum_nights                            1     16756.532    180096.973    5124097.407    0.703        0.694 
## reviews_per_month                         1     16767.351    216700.214    5160700.648    0.700        0.692 
## ------------------------------------------------------------------------------------------------------------
## 
## - cleaning_fee:bathrooms 
## 
## 
##   Step 11 : AIC = 16702.86 
##  price ~ cleaning_fee + bathrooms + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + host_is_superhost + review_scores_checkin + review_scores_value + reviews_per_month + cleaning_fee:accommodates + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + availability_30:minimum_nights + accommodates:cancellation_policy 
## 
## ------------------------------------------------------------------------------------------------------------
## Variable                                  DF       AIC         Sum Sq          RSS        R-Sq     Adj. R-Sq 
## ------------------------------------------------------------------------------------------------------------
## review_scores_location                    1     16702.859         0.000    4946315.539    0.713        0.705 
## host_is_superhost                         1     16701.950      3551.563    4949867.101    0.713        0.705 
## bathrooms                                 1     16702.378      4947.473    4951263.011    0.713        0.705 
## availability_30:minimum_nights            1     16702.428      5108.157    4951423.695    0.713        0.705 
## cleaning_fee:accommodates                 1     16702.741      6128.874    4952444.412    0.712        0.704 
## review_scores_value                       1     16703.945     10053.209    4956368.748    0.712        0.704 
## availability_30                           1     16704.328     11303.960    4957619.498    0.712        0.704 
## review_scores_checkin                     1     16706.560     18586.168    4964901.707    0.712        0.704 
## cleaning_fee:review_scores_cleanliness    1     16713.173     40235.951    4986551.489    0.710        0.702 
## review_scores_cleanliness                 1     16715.526     47960.758    4994276.296    0.710        0.702 
## cancellation_policy                       1     16710.020     49583.718    4995899.256    0.710        0.703 
## zipcode:review_scores_location            1     16707.605     87808.106    5034123.644    0.708        0.701 
## cleaning_fee                              1     16729.215     93140.369    5039455.908    0.707        0.699 
## zipcode                                   1     16710.070     95975.947    5042291.485    0.707        0.701 
## bathrooms:accommodates                    1     16739.396    127008.268    5073323.807    0.705        0.697 
## room_type                                 1     16749.485    167518.238    5113833.776    0.703        0.695 
## accommodates:cancellation_policy          1     16747.553    174483.318    5120798.856    0.703        0.695 
## minimum_nights                            1     16755.591    181351.396    5127666.934    0.702        0.694 
## reviews_per_month                         1     16765.683    215510.522    5161826.060    0.700        0.692 
## ------------------------------------------------------------------------------------------------------------
## 
## - host_is_superhost 
## 
## 
##   Step 12 : AIC = 16701.95 
##  price ~ cleaning_fee + bathrooms + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + review_scores_checkin + review_scores_value + reviews_per_month + cleaning_fee:accommodates + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + availability_30:minimum_nights + accommodates:cancellation_policy 
## 
## ------------------------------------------------------------------------------------------------------------
## Variable                                  DF       AIC         Sum Sq          RSS        R-Sq     Adj. R-Sq 
## ------------------------------------------------------------------------------------------------------------
## review_scores_location                    1     16701.950         0.000    4949867.101    0.713        0.705 
## bathrooms                                 1     16701.372      4633.932    4954501.034    0.712        0.705 
## availability_30:minimum_nights            1     16701.678      5631.475    4955498.577    0.712        0.705 
## cleaning_fee:accommodates                 1     16701.887      6313.049    4956180.150    0.712        0.704 
## review_scores_value                       1     16702.671      8870.870    4958737.971    0.712        0.704 
## availability_30                           1     16703.352     11092.475    4960959.576    0.712        0.704 
## review_scores_checkin                     1     16706.860     22553.477    4972420.578    0.711        0.704 
## cleaning_fee:review_scores_cleanliness    1     16712.140     39856.302    4989723.403    0.710        0.702 
## cancellation_policy                       1     16709.584     51175.231    5001042.332    0.710        0.702 
## review_scores_cleanliness                 1     16715.803     51895.940    5001763.041    0.710        0.702 
## zipcode:review_scores_location            1     16706.596     87538.183    5037405.285    0.708        0.701 
## cleaning_fee                              1     16728.726     94601.377    5044468.478    0.707        0.699 
## zipcode                                   1     16709.321     96578.767    5046445.868    0.707        0.701 
## bathrooms:accommodates                    1     16738.631    127582.905    5077450.006    0.705        0.697 
## room_type                                 1     16748.670    167956.887    5117823.988    0.703        0.695 
## accommodates:cancellation_policy          1     16746.455    173970.112    5123837.213    0.703        0.695 
## minimum_nights                            1     16756.975    189228.470    5139095.571    0.702        0.694 
## reviews_per_month                         1     16764.278    213980.396    5163847.498    0.700        0.692 
## ------------------------------------------------------------------------------------------------------------
## 
## - bathrooms 
## 
## 
##   Step 13 : AIC = 16701.37 
##  price ~ cleaning_fee + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + review_scores_checkin + review_scores_value + reviews_per_month + cleaning_fee:accommodates + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + availability_30:minimum_nights + accommodates:cancellation_policy 
## 
## ------------------------------------------------------------------------------------------------------------
## Variable                                  DF       AIC         Sum Sq          RSS        R-Sq     Adj. R-Sq 
## ------------------------------------------------------------------------------------------------------------
## review_scores_location                    1     16701.372         0.000    4954501.034    0.712        0.705 
## availability_30:minimum_nights            1     16701.134      5747.687    4960248.721    0.712        0.704 
## review_scores_value                       1     16701.914      8292.336    4962793.369    0.712        0.704 
## availability_30                           1     16702.789     11149.565    4965650.599    0.712        0.704 
## cleaning_fee:accommodates                 1     16704.866     17940.166    4972441.200    0.711        0.704 
## review_scores_checkin                     1     16706.381     22899.635    4977400.669    0.711        0.703 
## cleaning_fee:review_scores_cleanliness    1     16711.538     39814.689    4994315.723    0.710        0.702 
## review_scores_cleanliness                 1     16714.918     50931.324    5005432.358    0.709        0.702 
## cancellation_policy                       1     16709.151     51700.137    5006201.170    0.709        0.702 
## zipcode:review_scores_location            1     16706.245     88373.897    5042874.931    0.707        0.701 
## zipcode                                   1     16708.499     95855.962    5050356.995    0.707        0.700 
## cleaning_fee                              1     16740.632    136328.880    5090829.913    0.704        0.697 
## room_type                                 1     16746.870    163995.568    5118496.602    0.703        0.695 
## accommodates:cancellation_policy          1     16744.528    169582.083    5124083.116    0.703        0.695 
## minimum_nights                            1     16756.527    189845.935    5144346.969    0.701        0.693 
## reviews_per_month                         1     16765.504    220316.069    5174817.102    0.700        0.692 
## bathrooms:accommodates                    1     16863.578    565217.336    5519718.370    0.680        0.671 
## ------------------------------------------------------------------------------------------------------------
## 
## - availability_30:minimum_nights 
## 
## 
##   Step 14 : AIC = 16701.13 
##  price ~ cleaning_fee + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + review_scores_checkin + review_scores_value + reviews_per_month + cleaning_fee:accommodates + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + accommodates:cancellation_policy 
## 
## ------------------------------------------------------------------------------------------------------------
## Variable                                  DF       AIC         Sum Sq          RSS        R-Sq     Adj. R-Sq 
## ------------------------------------------------------------------------------------------------------------
## review_scores_location                    1     16701.134         0.000    4960248.721    0.712        0.704 
## review_scores_value                       1     16701.739      8505.888    4968754.610    0.712        0.704 
## cleaning_fee:accommodates                 1     16704.780     18458.234    4978706.955    0.711        0.704 
## review_scores_checkin                     1     16706.064     22665.259    4982913.981    0.711        0.703 
## availability_30                           1     16707.058     25925.652    4986174.373    0.711        0.703 
## cleaning_fee:review_scores_cleanliness    1     16711.190     39497.547    4999746.268    0.710        0.702 
## cancellation_policy                       1     16708.834     51497.542    5011746.263    0.709        0.702 
## review_scores_cleanliness                 1     16714.850     51551.574    5011800.295    0.709        0.702 
## zipcode:review_scores_location            1     16705.633     87230.200    5047478.921    0.707        0.701 
## zipcode                                   1     16707.896     94750.419    5054999.140    0.707        0.700 
## cleaning_fee                              1     16740.435    136623.750    5096872.472    0.704        0.696 
## room_type                                 1     16746.314    163113.336    5123362.057    0.703        0.695 
## accommodates:cancellation_policy          1     16743.904    168476.990    5128725.711    0.702        0.695 
## reviews_per_month                         1     16764.113    216644.476    5176893.197    0.699        0.692 
## minimum_nights                            1     16787.937    298424.390    5258673.112    0.695        0.687 
## bathrooms:accommodates                    1     16865.508    573757.291    5534006.012    0.679        0.670 
## ------------------------------------------------------------------------------------------------------------
## 
## 
## No more variables to be removed.
## 
## Variables Removed: 
## 
## - bed_type 
## - bathrooms:room_type 
## - review_scores_rating 
## - beds 
## - review_scores_accuracy 
## - host_listings_count 
## - review_scores_communication 
## - extra_people 
## - number_of_reviews 
## - accommodates 
## - cleaning_fee:bathrooms 
## - host_is_superhost 
## - bathrooms 
## - availability_30:minimum_nights 
## 
## 
## Final Model Output 
## ------------------
## 
##                          Model Summary                           
## ----------------------------------------------------------------
## R                       0.844       RMSE                 57.892 
## R-Squared               0.712       Coef. Var            44.041 
## Adj. R-Squared          0.704       MSE                3351.519 
## Pred R-Squared           -Inf       MAE                  38.371 
## ----------------------------------------------------------------
##  RMSE: Root Mean Square Error 
##  MSE: Mean Square Error 
##  MAE: Mean Absolute Error 
## 
##                                   ANOVA                                    
## --------------------------------------------------------------------------
##                     Sum of                                                
##                    Squares          DF    Mean Square      F         Sig. 
## --------------------------------------------------------------------------
## Regression    12264095.479          39     314463.987    93.827    0.0000 
## Residual       4960248.721        1480       3351.519                     
## Total         17224344.200        1519                                    
## --------------------------------------------------------------------------
## 
##                                                             Parameter Estimates                                                              
## --------------------------------------------------------------------------------------------------------------------------------------------
##                                                       model       Beta    Std. Error    Std. Beta      t        Sig        lower      upper 
## --------------------------------------------------------------------------------------------------------------------------------------------
##                                                 (Intercept)     72.158        18.691                  3.861    0.000      35.495    108.822 
##                                                cleaning_fee      0.563         0.088        0.285     6.385    0.000       0.390      0.736 
##                                       room_typePrivate room    -25.810         3.872       -0.110    -6.667    0.000     -33.405    -18.216 
##                                        room_typeShared room    -64.031        22.566       -0.041    -2.837    0.005    -108.296    -19.766 
##                                   review_scores_cleanliness     14.334         3.655        0.377     3.922    0.000       7.165     21.503 
##                                                zipcode28715    -38.506        59.334       -0.048    -0.649    0.516    -154.893     77.881 
##                                                zipcode28732     80.321        37.599        0.092     2.136    0.033       6.569    154.073 
##                                                zipcode28748    -29.032        58.557       -0.007    -0.496    0.620    -143.896     85.832 
##                                                zipcode28787     29.228        58.912        0.007     0.496    0.620     -86.331    144.787 
##                                                zipcode28801     39.795        20.361        0.157     1.954    0.051      -0.145     79.735 
##                                                zipcode28803     71.589        21.049        0.233     3.401    0.001      30.300    112.878 
##                                                zipcode28804     15.780        23.344        0.048     0.676    0.499     -30.012     61.571 
##                                                zipcode28805      1.963        25.537        0.006     0.077    0.939     -48.130     52.056 
##                                                zipcode28806      6.664        20.486        0.029     0.325    0.745     -33.520     46.849 
##                                                zipcode28815     45.637        58.662        0.011     0.778    0.437     -69.432    160.706 
##                                                zipcode29710      7.148        60.865        0.002     0.117    0.907    -112.242    126.538 
##                                      review_scores_location      4.256         4.347        0.111     0.979    0.328      -4.271     12.783 
##                                             availability_30      0.537         0.193        0.040     2.781    0.005       0.158      0.915 
##                                              minimum_nights     -1.884         0.200       -0.146    -9.436    0.000      -2.275     -1.492 
##                                 cancellation_policymoderate      2.783         6.557        0.013     0.425    0.671     -10.078     15.645 
##              cancellation_policystrict_14_with_grace_period     -7.033         7.180       -0.031    -0.979    0.328     -21.118      7.052 
##                          cancellation_policysuper_strict_30    -58.862        37.197       -0.061    -1.582    0.114    -131.826     14.101 
##                          cancellation_policysuper_strict_60     76.707        25.346        0.099     3.026    0.003      26.989    126.426 
##                                       review_scores_checkin    -11.797         4.537       -0.310    -2.601    0.009     -20.696     -2.899 
##                                         review_scores_value     -6.006         3.770       -0.157    -1.593    0.111     -13.400      1.389 
##                                           reviews_per_month     -5.277         0.656       -0.132    -8.040    0.000      -6.565     -3.990 
##                                   cleaning_fee:accommodates     -0.022         0.009       -0.116    -2.347    0.019      -0.040     -0.004 
##                                      accommodates:bathrooms      6.413         0.490        0.489    13.084    0.000       5.452      7.375 
##                      cleaning_fee:review_scores_cleanliness     -0.026         0.008       -0.122    -3.433    0.001      -0.041     -0.011 
##                         zipcode28715:review_scores_location      1.861         6.225        0.022     0.299    0.765     -10.351     14.072 
##                         zipcode28732:review_scores_location     -9.569         4.141       -0.100    -2.311    0.021     -17.691     -1.447 
##                         zipcode28748:review_scores_location         NA         2.239        0.000     0.032    0.975          NA         NA 
##                         zipcode28787:review_scores_location         NA         2.329       -0.015    -2.659    0.008          NA         NA 
##                         zipcode28801:review_scores_location      0.071         2.554        0.039     0.410    0.682      -4.321      4.462 
##                         zipcode28803:review_scores_location     -6.193         2.752        0.031     0.366    0.715     -10.761     -1.625 
##                         zipcode28804:review_scores_location      1.048         2.260       -0.018    -0.275    0.783      -3.962      6.057 
##                         zipcode28805:review_scores_location      1.006         1.529        0.032     0.716    0.474      -4.393      6.405 
##                         zipcode28806:review_scores_location     -0.622         1.585        0.239     3.588    0.000      -5.056      3.812 
##                         zipcode28815:review_scores_location         NA         6.764        0.037     2.270    0.023          NA         NA 
##                         zipcode29710:review_scores_location         NA         3.382        0.000     6.402    0.000          NA         NA 
##                    cancellation_policymoderate:accommodates      1.095            NA        0.012        NA       NA      -1.904      4.094 
## cancellation_policystrict_14_with_grace_period:accommodates      5.688            NA       -0.603        NA       NA       2.578      8.798 
##             cancellation_policysuper_strict_30:accommodates     15.356            NA       -0.372        NA       NA       2.089     28.623 
##             cancellation_policysuper_strict_60:accommodates     21.650            NA        0.150        NA       NA      15.017     28.283 
## --------------------------------------------------------------------------------------------------------------------------------------------
final.interactions.model <- lm(price ~ cleaning_fee * accommodates + accommodates * bathrooms + cleaning_fee * review_scores_cleanliness + zipcode * review_scores_location + cancellation_policy * accommodates + host_is_superhost
+ zipcode
+ room_type
+ accommodates
+ bathrooms
+ cleaning_fee
+ minimum_nights
+ availability_30
+ review_scores_cleanliness
+ review_scores_checkin
+ review_scores_location
+ review_scores_value
+ reviews_per_month
+ cancellation_policy, data=train.airbnb)
kable(tidy(final.interactions.model), digits=3)
term estimate std.error statistic p.value
(Intercept) 61.451 21.132 2.908 0.004
cleaning_fee 0.503 0.098 5.140 0.000
accommodates 1.378 2.372 0.581 0.562
bathrooms 9.087 6.797 1.337 0.181
review_scores_cleanliness 14.170 3.697 3.832 0.000
zipcode28715 -35.282 59.369 -0.594 0.552
zipcode28732 80.679 37.606 2.145 0.032
zipcode28748 -29.403 58.563 -0.502 0.616
zipcode28787 30.147 58.963 0.511 0.609
zipcode28801 40.403 20.439 1.977 0.048
zipcode28803 71.606 21.067 3.399 0.001
zipcode28804 14.948 23.368 0.640 0.522
zipcode28805 4.086 25.625 0.159 0.873
zipcode28806 6.334 20.500 0.309 0.757
zipcode28815 43.110 58.695 0.734 0.463
zipcode29710 8.865 60.917 0.146 0.884
review_scores_location 4.304 4.354 0.989 0.323
cancellation_policymoderate 3.091 8.609 0.359 0.720
cancellation_policystrict_14_with_grace_period -6.105 9.132 -0.669 0.504
cancellation_policysuper_strict_30 -54.426 37.624 -1.447 0.148
cancellation_policysuper_strict_60 75.350 26.027 2.895 0.004
host_is_superhostt 3.844 3.519 1.092 0.275
room_typePrivate room -26.127 4.007 -6.521 0.000
room_typeShared room -70.252 23.427 -2.999 0.003
minimum_nights -1.859 0.201 -9.265 0.000
availability_30 0.527 0.193 2.726 0.006
review_scores_checkin -10.903 4.625 -2.357 0.019
review_scores_value -6.805 3.803 -1.789 0.074
reviews_per_month -5.370 0.676 -7.940 0.000
cleaning_fee:accommodates -0.013 0.011 -1.183 0.237
accommodates:bathrooms 5.278 0.979 5.393 0.000
cleaning_fee:review_scores_cleanliness -0.027 0.008 -3.473 0.001
zipcode28715:review_scores_location 1.457 6.230 0.234 0.815
zipcode28732:review_scores_location -9.638 4.141 -2.327 0.020
zipcode28801:review_scores_location -0.041 2.245 -0.018 0.985
zipcode28803:review_scores_location -6.223 2.331 -2.670 0.008
zipcode28804:review_scores_location 1.085 2.555 0.425 0.671
zipcode28805:review_scores_location 0.746 2.759 0.270 0.787
zipcode28806:review_scores_location -0.642 2.261 -0.284 0.776
accommodates:cancellation_policymoderate 0.868 2.340 0.371 0.711
accommodates:cancellation_policystrict_14_with_grace_period 5.412 2.367 2.286 0.022
accommodates:cancellation_policysuper_strict_30 14.608 6.965 2.097 0.036
accommodates:cancellation_policysuper_strict_60 21.410 3.808 5.623 0.000
summary(final.interactions.model)$adj.r.squared
## [1] 0.7044265

Assumptions

train.airbnb <- train.airbnb %>% mutate(stand.resid = rstandard(final.interactions.model),
                                        pred = predict(final.interactions.model))
ggplot(data = train.airbnb, aes(x=stand.resid)) + geom_histogram()
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 2 rows containing non-finite values (stat_bin).

qqnorm(train.airbnb$stand.resid)

p1 <- ggplot(data = train.airbnb, aes(x=pred, y=stand.resid)) + geom_point() + 
  labs(x="Predicted", y="Residual", title="Residuals vs Predicted",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))

p2 <- ggplot(data = train.airbnb, aes(x=host_is_superhost, y=stand.resid)) + geom_point() + 
  labs(x="Predicted", y="Residual", title="Residuals vs Superhost",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))

p3 <- ggplot(data = train.airbnb, aes(x=zipcode, y=stand.resid)) + geom_point() + 
  labs(x="Predicted", y="Residual", title="Residuals vs Zipcode",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))

p4 <- ggplot(data = train.airbnb, aes(x=room_type, y=stand.resid)) + geom_point() + 
  labs(x="Predicted", y="Residual", title="Residuals vs Room Type",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))

p5 <- ggplot(data = train.airbnb, aes(x=accommodates, y=stand.resid)) + geom_point() + 
  labs(x="Number of Guests", y="Residual", title="Residuals vs Accommodates",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))

p6 <- ggplot(data = train.airbnb, aes(x=bathrooms, y=stand.resid)) + geom_point() + 
  labs(x="Number of Bathrooms", y="Residual", title="Residuals vs Bathrooms",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))

p7 <- ggplot(data = train.airbnb, aes(x= cleaning_fee, y=stand.resid)) + geom_point() + 
  labs(x="Fee ($)", y="Residual", title="Residuals vs Cleaning Fee",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))

p8 <-ggplot(data = train.airbnb, aes(x=minimum_nights, y=stand.resid)) + geom_point() + 
  labs(x="Minimum Nights", y="Residual", title="Residuals vs Minimum_nights",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))

p9 <- ggplot(data = train.airbnb, aes(x=availability_30, y=stand.resid)) + geom_point() + 
  labs(x="Number of Available Nights in the next month", y="Residual", title="Residuals vs Availability",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))

p10 <- ggplot(data = train.airbnb, aes(x=review_scores_cleanliness, y=stand.resid)) + geom_point() + 
  labs(x="Cleanliness Review (out of 100%)", y="Residual", title="Residuals vs Cleanliness Review Scores",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))

p11 <- ggplot(data = train.airbnb, aes(x=review_scores_checkin, y=stand.resid)) + geom_point() + 
  labs(x="Check-In Review (out of 100%)", y="Residual", title="Residuals vs Check-In Review Scores",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))

p12 <- ggplot(data = train.airbnb, aes(x=review_scores_location, y=stand.resid)) + geom_point() + 
  labs(x="Location Review (out of 100%)", y="Residual", title="Residuals vs Location Review Scores",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))

p13 <- ggplot(data = train.airbnb, aes(x=review_scores_value, y=stand.resid)) + geom_point() + 
  labs(x="Value Review (out of 100%)", y="Residual", title="Residuals vs Value Review Scores",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))

p14 <- ggplot(data = train.airbnb, aes(x=reviews_per_month, y=stand.resid)) + geom_point() + 
  labs(x="Reviews per month", y="Residual", title="Residuals vs Reviews per month",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))

p15 <- ggplot(data = train.airbnb, aes(x=cancellation_policy, y=stand.resid)) + geom_point() + 
  labs(x="Cancellation Policy", y="Residual", title="Residuals vs Cancellation Policy",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))
plot_grid(p1,p2,p3,p4)
## Warning: Removed 2 rows containing missing values (geom_point).

## Warning: Removed 2 rows containing missing values (geom_point).

## Warning: Removed 2 rows containing missing values (geom_point).

## Warning: Removed 2 rows containing missing values (geom_point).

plot_grid(p5,p6,p7,p8)
## Warning: Removed 2 rows containing missing values (geom_point).

## Warning: Removed 2 rows containing missing values (geom_point).

## Warning: Removed 2 rows containing missing values (geom_point).

## Warning: Removed 2 rows containing missing values (geom_point).

plot_grid(p9,p10,p11,p12)
## Warning: Removed 2 rows containing missing values (geom_point).

## Warning: Removed 2 rows containing missing values (geom_point).

## Warning: Removed 2 rows containing missing values (geom_point).

## Warning: Removed 2 rows containing missing values (geom_point).

plot_grid(p13,p14,p15)
## Warning: Removed 2 rows containing missing values (geom_point).

## Warning: Removed 2 rows containing missing values (geom_point).

## Warning: Removed 2 rows containing missing values (geom_point).

plots - log cleaning fee

  1. Constant variance

  2. Normality

  3. Independence

  4. Leverage Points/ outliers

train.airbnb <- train.airbnb %>%
  mutate(leverage = hatvalues(final.interactions.model), 
         cooks = cooks.distance(final.interactions.model),
         obs.num = row_number())

ggplot(data=train.airbnb, aes(x=obs.num,y=leverage)) + 
  geom_point(alpha=0.5) + 
  geom_hline(yintercept=0.,color="red")+
  labs(x="Observation Number",y="Leverage",title="Leverage")

ggplot(data=train.airbnb, aes(x=obs.num,y=cooks)) + 
  geom_point() + 
  geom_hline(yintercept=1,color="red")+
  labs(x="Observation Number",y="Cook's Distance",title="Cook's Distance")
## Warning: Removed 2 rows containing missing values (geom_point).

Prediction

#Predict on the testing set using our final model
test.predict <- predict(final.interactions.model, test.airbnb)
test.predict
##          7         10         11         14         15         17 
##   84.64052   72.96663  102.72190   78.52439   89.19559  117.61594 
##         24         55         57         61         71         77 
##  141.15764  100.28196   70.92001  224.60673   79.85453  106.31731 
##         84         87         89         90         93        104 
##   71.59174  302.03480   90.10250   97.18453   99.08798   64.56191 
##        111        128        130        138        142        143 
##   63.94932  191.76197  116.01474  241.35576   83.67427   92.82605 
##        146        149        156        157        159        164 
##  116.78299  208.14729   29.03607  130.48794  131.96472   96.55231 
##        166        168        177        180        181        182 
##  321.77135  169.97883  133.93311   54.22461  171.37529  123.24628 
##        187        188        195        196        199        202 
##   83.13879  129.41183   96.90332   91.73163  107.26555  137.12288 
##        204        214        215        216        217        220 
##   71.82477  120.39849  276.16711   78.20739   90.64574  225.68201 
##        228        231        233        239        260        268 
##  101.49181   74.62224  122.68531   87.03995   70.66253   95.91687 
##        273        290        293        295        301        306 
##   86.05838   64.83063   92.62470  108.08154   95.14538  132.09267 
##        309        312        316        319        324        326 
##   69.90011   89.93865   70.27217   87.88358   60.84089  116.65538 
##        334        338        346        353        354        365 
##   95.25934   77.80644   80.90395  171.48064  103.46610   58.36418 
##        369        378        384        387        394        396 
##   64.31004  141.30848  227.13629   67.63267  209.16643  120.36850 
##        401        404        407        412        422        424 
##   62.92323   33.90318   83.40873  134.75908  105.34516  128.93890 
##        426        433        447        450        454        458 
##  136.50455   42.16275  199.96111  115.05603  219.41021  135.58990 
##        460        461        482        483        484        492 
##   95.03399  123.77645  211.99139  100.20501  178.80776   89.10496 
##        493        497        500        508        512        518 
##  273.77523  163.64672   71.04001   50.73351  129.65041  109.74796 
##        531        541        547        560        561        563 
##   76.82616  145.36560  196.41867   86.10256  140.93783   86.02805 
##        567        568        577        578        591        595 
##  173.28485  132.05294  194.27134  163.73483   88.87943   40.22509 
##        604        612        613        617        631        640 
##  171.16731  128.47950  117.40654   90.21837  110.75231  135.71472 
##        647        649        651        664        670        671 
##  156.83681   59.79595  108.53126  107.51490  108.21864  332.88143 
##        678        681        689        690        692        700 
##  155.65743  156.14516  103.67694   97.34390  116.12719  104.94929 
##        702        713        717        724        728        731 
##  140.75709   79.45901  149.76556   51.54717   94.99855  183.49013 
##        732        736        742        743        761        764 
##  149.09961   83.75986  126.04775   58.61166  193.95938  143.61859 
##        776        777        778        781        794        800 
##   59.41710  205.17372  147.35860   95.99342  354.90793   97.89456 
##        808        810        819        825        826        832 
##  170.69947   59.32438   53.75622   60.38406 1291.68477  355.83536 
##        833        835        843        846        848        852 
##  826.93616  610.24315   26.91883  124.32266  143.49292  108.83741 
##        855        857        860        861        863        872 
##   89.84914  266.97167  199.13793  109.14788   96.09790  143.64021 
##        873        875        877        881        883        902 
##   86.12498   90.87021  105.69155  191.64540   76.14289  196.62050 
##        905        918        926        934        941        954 
##  378.75351  125.03931   58.39207  102.91001  118.03705   94.87281 
##        957        962        967        968        976        985 
##  135.76017   73.19486  155.78060   92.65644   61.89308   52.98880 
##        996        997        999       1003       1004       1006 
##  107.85574  146.63354   96.61649   75.78195  171.06713  150.37027 
##       1012       1014       1023       1025       1033       1038 
##   88.43676  239.25412  144.33841  130.77156  113.50738  121.20226 
##       1041       1045       1054       1057       1065       1066 
##  127.55646  183.09697   56.37037   58.83709  100.10278  199.46504 
##       1073       1079       1086       1095       1096       1101 
##   63.22049  110.55147  119.21605  200.76808  105.03937   83.67371 
##       1109       1113       1114       1118       1125       1127 
##  158.23133  103.28347  402.71484   44.70723  126.42077  121.58268 
##       1131       1136       1137       1139       1158       1160 
##   70.96992  149.30354   93.79841   85.06672  284.03715  219.19036 
##       1164       1167       1168       1181       1183       1190 
##   95.31415  111.68987   54.94526  114.51867   85.85812  167.48953 
##       1197       1204       1210       1212       1216       1231 
##  118.39270   61.61760  126.38238  121.66276  223.28282   68.68112 
##       1240       1248       1249       1251       1253       1256 
##  132.81735  144.93602  122.06857  121.94349  100.49788   86.16948 
##       1257       1262       1267       1274       1277       1283 
##   57.04636  478.38258  119.02355  142.79454  173.21395  125.60977 
##       1285       1291       1295       1299       1312       1315 
##   71.88676  116.70462   82.80134   28.08041  141.91871  151.41953 
##       1316       1321       1323       1324       1330       1333 
##  155.74949  133.84965  159.86290   53.44670   41.74258  139.42622 
##       1355       1358       1370       1371       1373       1379 
##   54.36748  120.29005   84.17785  116.48461   57.58637  123.15114 
##       1380       1387       1388       1397       1401       1416 
##  342.51711   33.85530  298.47823  132.05739  140.68136   85.48464 
##       1419       1421       1422       1423       1426       1429 
##   94.10036   94.04032   83.23148  132.35771  213.10800  162.59183 
##       1440       1446       1450       1461       1470       1471 
##  232.04987   95.76610   58.36679  118.91689   88.36015  115.91342 
##       1473       1483       1490       1492       1494       1497 
##  231.45314  154.49012  115.68984   87.08570  124.12264   71.48686 
##       1498       1501       1502       1507       1516       1518 
##  109.43765  101.12543  830.01885  109.35934   85.88425   96.67278 
##       1519       1523       1529       1530       1536       1537 
##  188.55252  152.21343   98.99996  166.86243  123.94426   64.85362 
##       1540       1542       1547       1548       1552       1555 
##  235.52346  128.23102   98.99846   25.19179   98.36552   69.49994 
##       1571       1581       1588       1589       1590       1591 
##  134.78513   93.90992   87.69848  218.56372  146.95380  100.77579 
##       1596       1599       1608       1615       1631       1632 
##   60.03465  170.91253  107.35875  126.14031   95.73617   77.05347 
##       1633       1646       1649       1653       1655       1660 
##   68.49891   70.57940  330.32876   44.75119   82.17580  154.36102 
##       1663       1664       1672       1674       1677       1679 
##   95.86411  385.88675   90.05177   89.79365  124.54784   88.17013 
##       1680       1687       1706       1707       1721       1726 
##   19.96967  105.27390   46.98837   77.31393   98.20966   67.11996 
##       1728       1730       1733       1734       1740       1744 
##  217.96603   22.55754  161.96057   81.58878  160.25164   70.01736 
##       1756       1758       1759       1763       1765       1767 
##   81.01858  200.62860  158.40415   87.58774  148.12821  290.94031 
##       1770       1772       1779       1781       1784       1794 
##  114.86574  213.42622  141.22991   43.01172  204.59672  113.03789 
##       1799       1807       1808       1813       1816       1840 
##  362.42630  362.15354   94.45507   86.71005  341.44847   47.45854 
##       1847       1853       1856       1858       1859       1861 
##  133.33555  187.29630  130.62448  153.53141   85.95288  161.38745 
##       1890       1891       1897       1898       1899       1902 
##  120.23151  230.45598  127.25131  318.98920  122.65381  312.37067 
##       1905       1906       1912       1919       1921       1925 
##   62.40026   76.41238  235.64398  209.53952  380.01928  148.03732 
##       1930       1932 
##  110.34180  105.30184